Wikiversity talk:Main Page

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{{attention}} To request an edit to the [[Wikiversity:Page protection|protected]] Main Page, add {{tl|editprotected}} to your request. Such requests should either be obvious or uncontroversial, or be discussed to show consensus, so please do not make vague requests here. If possible, describe exactly what changes should be made so that any custodian can quickly satisfy the request.&lt;br&gt;
{{attention}} To raise general topics about [[Wikiversity]], make general suggestions about Wikiversity, to ask questions, or to talk about anything else of a general nature, use the [[Wikiversity:Colloquium|Colloquium]].&lt;br&gt;
{{attention}} To discuss the structure, appearance, etc. of the [[Wikiversity:Main Page|Main Page]], go to the [[Wikiversity:Main page learning project]] and the [[Wikiversity talk:Main page learning project|talk page for the main page learning project]].
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'''''If you wish to post something below, go ahead. It's a talk page. But you are more likely to get a response by going to the [[Wikiversity:Colloquium|Colloquium]], which is where the main talking at Wikiversity goes on! See you there.'''''

{{archive box|
{{center top}}'''List of talk archives'''{{center bottom}}
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{{Special:Prefixindex/Wikiversity talk:Main Page/Archive |hideredirects=1|stripprefix=1}}
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== The Wikiversity:Main page learning project ==

The [[Wikiversity:Main page learning project]] was launched after the redesign of the main page in December 2007. The [[Wikiversity:Main page learning project]] has as its goal &quot;the promotion of responsible involvement of the Wikiversity community in an efficient, productive, open and inclusive maintenance of the Wikiversity main page as a flagship of the activity and values of the Wikiversity community&quot;. If you would like to get involved in the design of the main page, this is where to go. 

If you have general comments about the main page, but you don't especially want to get involved in the main page project, then you can also leave comments on the [[Wikiversity_talk:Main page learning project|talk page for the main page learning project]].

:I've suggested that it might be time to retire the &quot;quote of the day&quot; project and remove the quotes from the Main Page. See: [[Wikiversity talk:Main page learning project/QOTD]]. It might also be appropriate to deprecate the inactive [[Wikiversity:Main page learning project]] and archive it. Thoughts? --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 23:37, 29 November 2019 (UTC)

== add new language university ==
Now that Chinese Wikiversity is created, please add a cross-wiki link to it. --[[User:WQL|WQL]] ([[User talk:WQL|discuss]] • [[Special:Contributions/WQL|contribs]]) 12:52, 12 August 2018 (UTC)

:{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 14:29, 12 August 2018 (UTC)
::What about zulu language [[User:Lucky Shabalala|Lucky Shabalala]] ([[User talk:Lucky Shabalala|discuss]] • [[Special:Contributions/Lucky Shabalala|contribs]]) 05:57, 30 April 2025 (UTC)

== Edit request from 204.234.101.112, 14 February 2019 ==

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[[Special:Contributions/204.234.101.112|204.234.101.112]] ([[User talk:204.234.101.112|discuss]]) 21:17, 14 February 2019 (UTC)

:{{Not done}} Empty request -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 01:11, 15 February 2019 (UTC)

== Georgian (ka) wikiversity ==
PLEASE 

Help me to make Georgian (ka) wikiversity--[[User:ჯეო|ჯეო]] ([[User talk:ჯეო|discuss]] • [[Special:Contributions/ჯეო|contribs]]) 17:23, 1 March 2019 (UTC)

:{{at|ჯეო}} See https://beta.wikiversity.org/wiki/Main_Page. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:00, 1 March 2019 (UTC)

დიდი მადლობა (Didi Madloba-Thank You)!--[[User:ჯეო|ჯეო]] ([[User talk:ჯეო|discuss]] • [[Special:Contributions/ჯეო|contribs]]) 08:44, 2 March 2019 (UTC)

::Please see [[betawikiversity:Category:KA]]. That is the appropriate place to create learning pages in this language. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 14:11, 10 March 2019 (UTC)

== new langueages ==

we should admit crosing of languajes to have a better understanding--[[Special:Contributions/201.208.239.198|201.208.239.198]] ([[User talk:201.208.239.198|discuss]]) 19:34, 25 July 2019 (UTC)

:This is the English Wikiversity. See [[:es:Portada|Wikiversidad]] for Wikiversity in Spanish. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 22:39, 25 July 2019 (UTC)

== How to change an username? ==

How to change an username? --[[User:Josephina Phoebe White|Josephina Phoebe White]] ([[User talk:Josephina Phoebe White|discuss]] • [[Special:Contributions/Josephina Phoebe White|contribs]]) 07:27, 28 August 2019 (UTC)
*{{ping|Josephina Phoebe White}} You can request at [[Special:GlobalRenameRequest]] --[[User:94rain|94rain]] ([[User talk:94rain|discuss]] • [[Special:Contributions/94rain|contribs]]) 07:29, 28 August 2019 (UTC)
Thanks. --[[User:Josephina Phoebe White|Josephina Phoebe White]] ([[User talk:Josephina Phoebe White|discuss]] • [[Special:Contributions/Josephina Phoebe White|contribs]]) 07:45, 28 August 2019 (UTC)

==Religious user names allowed in Wikiversity?==

https://en.m.wikiversity.org/wiki/Wikiversity:Username

Names of religious figures such as &quot;God&quot;, &quot;Jehovah&quot;,&quot;Buddha&quot;,&quot;Jainism&quot;,&quot;Bonadea&quot;,Hinduism or &quot;Allah&quot;, which user names prohibited

Please answer for my question. This Wikiversity user name policy still alive? Religious user names are prohibited? 

:It isn't a policy, but it's a guideline for people who are wanting to register an account are recommended to follow (as per the page, which could be changed with community consensus). I see no reason for this statement to be &quot;dead&quot;. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 00:15, 2 September 2019 (UTC)
::: Yes: Religious user names are under hedding &quot;Inflammatory usernames&quot;, will be blocked and not allowed.

== LinkedIn ==

I insist that a Wikiversity page should be added on LinkedIn. Wikimedia has its LinkedIn page; Wikipedia, too. But not Wikiversity. I tried to show my Swedish studies but could not choose Wikiversity as the Institution. Why not? Even when it is not a &quot;granting degree&quot; Institution, is is still an Institution, right? When I contacted LinkedIn about this, they sent me the link so that I can create myself the Wikiversity page. But then there is box I must tick: &quot; I confirm I am an approved authority of this Institution to create this page&quot;, which is not the case. But I think there are many Wikiversity experts on here that woud qualify as Wikiversity Linkedin page creators. I can create the page if someone here approves, but I would need some info: # of employees, etc. --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 23:34, 18 January 2020 (UTC)

:The information would go here [https://www.linkedin.com/company/setup/new/ Wikiversity institution] but it probably should have a bureaucrat or someone from the WMF tick &quot;I verify that I am an authorized representative of this organization and have the right to act on its behalf in the creation and management of this page. The organization and I agree to the additional terms for Pages.&quot; The number of employees (volunteers is not an option but we are unpaid) for our Wikiversity I guess could be the number of active users 201-500. The current logo is File:Wikiversity logo 2017.svg. The website can be https://en.wikiversity.org/wiki/Wikiversity:Main_Page.--[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 00:16, 19 January 2020 (UTC)

{{At|Leonardo T. Cardillo}} Wikiversity is a community. None of us gets to insist that anything happen on behalf of the community unless there is consensus to do so. This requires a discussion in the [[Wikiversity:Colloquium]] and a vote for support or lack thereof. Because this request involves an outside organization, it may also require support from the WMF.

I have some concerns at this point that your passion regarding this issue far exceeds your demonstrated commitment to either Wikiversity or the wider Wikimedia community. It might be better to let this rest for a bit and learn more about how Wikiversity functions before insisting that this be discussed. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 03:29, 19 January 2020 (UTC)

:{{At|Dave Braunschweig}}: I apologize for the use of the word &quot;insist&quot;, I have taken note to not use it anymore here to avoid distractions from the main topic of conversation. Also, I do not like you judge how much my passions should go against my level of contributions. With that being said, and for my personal learning on this environment, can someone please guide me on the very first step I should take to have a Wikiversity page created on LinkedIn? I think you mentioned something like a &quot;poll&quot;, how do I do that? --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 04:38, 19 January 2020 (UTC)

::{{At|Leonardo T. Cardillo}} I have already guided you on the next step to take. Please read my response carefully. Then slow down and learn more about Wikiversity. We often have people come in with high passions and quick fixes that Wikiversity must make in order to improve. They're typically gone within a month and we're left having to clean up after them. That's not to suggest that this is or isn't a good idea. It is simply to point out that this is a community. You must first learn to work with the community before you try to change it. We look forward to working with you as you figure this out. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 15:31, 19 January 2020 (UTC)

:::{{At|Dave Braunschweig}} Thanks so much for your inputs. I have created this: https://en.wikiversity.org/wiki/Wikiversity:Colloquium#LinkedIn. Please indicate if that is the next step that was intended to be created. Also, please guide on the following ones. Best regards, --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 16:27, 19 January 2020 (UTC)

== Add New Language ==

Why not bn.wikiversity?  But there is Hindi!  Make it, please.  I am ready to cooperate if needed. [[User:Hirok Raja|Hirok Raja]] ([[User talk:Hirok Raja|discuss]] • [[Special:Contributions/Hirok Raja|contribs]]) 03:07, 1 August 2020 (UTC)

:[[User:Hirok Raja|Hirok Raja]]: please see [[:betawikiversity:|Wikiversity Beta]]. &amp;mdash;Hasley&amp;nbsp;[[user talk:Hasley|&lt;span style=&quot;color: #0645AD; vertical-align: super; font-size: smaller;&quot;&gt;talk&lt;/span&gt;]] 13:04, 1 August 2020 (UTC)

:{{At|Hirok Raja}} Also see [[meta:Wikiversity]]. We are the English Wikiversity. We have no role in setting up new Wikiversity languages. When bn.wikiversity is added, please let us know, and we will add it to our main page. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:59, 1 August 2020 (UTC)

== I'm learning Turkish🤩 ==

Hi(to the person reading this)! I'm learning Turkish and I would like someone(native Turkish speaker) to teach how to pronounce Turkish. I do know some words,alphabets and number☺️ and I'm still learning and I hope someone is willing to help me🥺.

@JinahJady! [[User:JanehJody|JanehJody]] ([[User talk:JanehJody|discuss]] • [[Special:Contributions/JanehJody|contribs]]) 18:14, 4 February 2021 (UTC)

:Hi. Welcome to Wikiversity! Please see our [[Turkish|resources relating to the study of the Turkish language]]. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:41, 4 February 2021 (UTC)
::Hi,@[[User:JanehJody|JanehJody]] can i help you ::) [[User:MexmetW|MexmetW]] ([[User talk:MexmetW|discuss]] • [[Special:Contributions/MexmetW|contribs]]) 07:47, 28 September 2022 (UTC)
:Hi,@[[User:JanehJody|JanehJody]] I would love to help you to learning turkish :) [[Special:Contributions/85.105.185.109|85.105.185.109]] ([[User talk:85.105.185.109|discuss]]) 07:31, 28 September 2022 (UTC)

== Is it Wikipedia remodeled or a copy of wikipedia? ==

I am confused--[[User:Noukden|Noukden]] ([[User talk:Noukden|discuss]] • [[Special:Contributions/Noukden|contribs]]) 20:45, 24 May 2021 (UTC)

:{{At|Noukden}} None of the above. See [[What is Wikiversity?]] and [[What Wikiversity is not]]. Wikiversity is learning projects. Link to Wikipedia rather than duplicating it and then add hands-on activities so users can learn by doing. See [[IT Fundamentals]] for one approach. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:15, 25 May 2021 (UTC)

== Action in the earliest? ==

I want to know much more of all action that happend in the earliest centuries. [[User:Dilbkhay|Dilbkhay]] ([[User talk:Dilbkhay|discuss]] • [[Special:Contributions/Dilbkhay|contribs]]) 14:57, 21 August 2021 (UTC)

:Depending upon what you mean by &quot;earliest&quot;, have a look at [[Paleanthropology]] or [[Philosophy/Sciences]]. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 21:07, 20 September 2021 (UTC)

== Biology ==

What are the basic principles of ecology [[User:Aludriyo Dominic|Aludriyo Dominic]] ([[User talk:Aludriyo Dominic|discuss]] • [[Special:Contributions/Aludriyo Dominic|contribs]]) 18:25, 25 January 2022 (UTC)

:{{At|Aludriyo Dominic}} Welcome! See [[Wikipedia:Ecology]]. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:17, 26 January 2022 (UTC)
:{{ping|Aludriyo Dominic}} I invite you to read [[User:Atcovi/Science/Ecology]] if you're interested in learning about the basics of Ecology. Also check out the wikipedia link above and [[:Category:Ecology|this category]]. Thanks and weclome! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 03:44, 26 January 2022 (UTC)

I will try to study [[User:Aludriyo Dominic|Aludriyo Dominic]] ([[User talk:Aludriyo Dominic|discuss]] • [[Special:Contributions/Aludriyo Dominic|contribs]]) 05:41, 28 January 2022 (UTC)

== Physics ==

Physics Can Be defined as A Pure Science Subject That deals with the Measurement Of Matter In relation to energy. --{{Unsigned|Oyeyemi Abdul-warith|29 January 2022}}

: Welcome to Wikiversity! Here is a landing page that may be helpful: [[Physics]]. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 16:42, 29 January 2022 (UTC)

== Popularize ==

Can someone popularize California or the State of Washington on the Main Page? [[Special:Contributions/2604:3D08:6286:7500:B441:2710:77A4:1304|2604:3D08:6286:7500:B441:2710:77A4:1304]] ([[User talk:2604:3D08:6286:7500:B441:2710:77A4:1304|discuss]]) 03:33, 26 June 2022 (UTC)

:No, sorry, promotion isn't part of the [[Wikiversity:Mission]]. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 12:06, 26 June 2022 (UTC)

== [[w:Armistice of WWI|Armistice of WWI]], [[w:Paris Peace Conference|Paris Peace Conference]] and Aftermath ==

The best time to feature this on the main page was last week or yesterday;  the second best time is today.

* [[w:Template:First_World_War_treaties]]  (this template should get transcluded or copied to wikiversity, since this doesn't work: {{w:First_World_War_treaties}} although I wish it would)
* [[Wikiversity:Colloquium#Proclaiming_Armistice_of_WWI_Remembrance_and_Veterans_Day_for_11th_Nov]] our course on WWI is woefully inadequate, but this is a good time to start improving it!
[[User:Jaredscribe|Jaredscribe]] ([[User talk:Jaredscribe|discuss]] • [[Special:Contributions/Jaredscribe|contribs]]) 10:22, 12 November 2023 (UTC)

== Can you please add isiZulu plz ==

Because all othere languages her so i can umderstand batter  [[User:Lucky Shabalala|Lucky Shabalala]] ([[User talk:Lucky Shabalala|discuss]] • [[Special:Contributions/Lucky Shabalala|contribs]]) 06:06, 30 April 2025 (UTC)

:Add it how? Add more resources to learn the language? I think that would be fantastic, but it's very labor-intensive and I doubt anyone here has the competence to add that kind of material. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 08:40, 30 April 2025 (UTC)

== banner ==

says set learning free, propare grammer would be Start learning for free [[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 20:21, 3 February 2026 (UTC)

:I'm a native American English speaker and this banner is grammatical. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 08:52, 4 February 2026 (UTC)
::That’s not the problem. I’m wondering if we should more clearly emphasize what Wikiversity is on this banner. Idk maybe it’s fine as it is I would just like it to be clearer[[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 16:15, 4 February 2026 (UTC)
:::nevermind i just got the banner thought it was supposed to say start learning free, but its actually set learning free(like release learning) [[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 16:12, 6 February 2026 (UTC)

== Amazon Brand Registry Service ==

Protecting your brand on Amazon starts with proper registration. Bizistech offers professional Amazon Brand Registry Services to help sellers secure brand ownership, access advanced brand tools, and protect products from unauthorized sellers. Our experts simplify the registration process, helping businesses strengthen their brand presence and grow confidently on Amazon. [[User:Bizistech92|Bizistech92]] ([[User talk:Bizistech92|discuss]] • [[Special:Contributions/Bizistech92|contribs]]) 04:56, 15 June 2026 (UTC)</text>
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      <comment>Reverted edit by [[Special:Contributions/Bizistech92|Bizistech92]] ([[User_talk:Bizistech92|talk]]) to last version by [[User:PieWriter|PieWriter]] using [[Wikiversity:Rollback|rollback]]</comment>
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{{attention}} To request an edit to the [[Wikiversity:Page protection|protected]] Main Page, add {{tl|editprotected}} to your request. Such requests should either be obvious or uncontroversial, or be discussed to show consensus, so please do not make vague requests here. If possible, describe exactly what changes should be made so that any custodian can quickly satisfy the request.&lt;br&gt;
{{attention}} To raise general topics about [[Wikiversity]], make general suggestions about Wikiversity, to ask questions, or to talk about anything else of a general nature, use the [[Wikiversity:Colloquium|Colloquium]].&lt;br&gt;
{{attention}} To discuss the structure, appearance, etc. of the [[Wikiversity:Main Page|Main Page]], go to the [[Wikiversity:Main page learning project]] and the [[Wikiversity talk:Main page learning project|talk page for the main page learning project]].
&lt;/div&gt;

----
'''''If you wish to post something below, go ahead. It's a talk page. But you are more likely to get a response by going to the [[Wikiversity:Colloquium|Colloquium]], which is where the main talking at Wikiversity goes on! See you there.'''''

{{archive box|
{{center top}}'''List of talk archives'''{{center bottom}}
{{Col list|3|
{{Special:Prefixindex/Wikiversity talk:Main Page/Archive |hideredirects=1|stripprefix=1}}
}}
{{SearchWithPrefix|prefix=Wikiversity talk:Main Page/|resourceName=talk archive}}
}}

== The Wikiversity:Main page learning project ==

The [[Wikiversity:Main page learning project]] was launched after the redesign of the main page in December 2007. The [[Wikiversity:Main page learning project]] has as its goal &quot;the promotion of responsible involvement of the Wikiversity community in an efficient, productive, open and inclusive maintenance of the Wikiversity main page as a flagship of the activity and values of the Wikiversity community&quot;. If you would like to get involved in the design of the main page, this is where to go. 

If you have general comments about the main page, but you don't especially want to get involved in the main page project, then you can also leave comments on the [[Wikiversity_talk:Main page learning project|talk page for the main page learning project]].

:I've suggested that it might be time to retire the &quot;quote of the day&quot; project and remove the quotes from the Main Page. See: [[Wikiversity talk:Main page learning project/QOTD]]. It might also be appropriate to deprecate the inactive [[Wikiversity:Main page learning project]] and archive it. Thoughts? --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 23:37, 29 November 2019 (UTC)

== add new language university ==
Now that Chinese Wikiversity is created, please add a cross-wiki link to it. --[[User:WQL|WQL]] ([[User talk:WQL|discuss]] • [[Special:Contributions/WQL|contribs]]) 12:52, 12 August 2018 (UTC)

:{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 14:29, 12 August 2018 (UTC)
::What about zulu language [[User:Lucky Shabalala|Lucky Shabalala]] ([[User talk:Lucky Shabalala|discuss]] • [[Special:Contributions/Lucky Shabalala|contribs]]) 05:57, 30 April 2025 (UTC)

== Edit request from 204.234.101.112, 14 February 2019 ==

&lt;nowiki&gt;{{editprotected}}&lt;/nowiki&gt;
&lt;!-- Begin request --&gt;


&lt;!-- End request --&gt;
[[Special:Contributions/204.234.101.112|204.234.101.112]] ([[User talk:204.234.101.112|discuss]]) 21:17, 14 February 2019 (UTC)

:{{Not done}} Empty request -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 01:11, 15 February 2019 (UTC)

== Georgian (ka) wikiversity ==
PLEASE 

Help me to make Georgian (ka) wikiversity--[[User:ჯეო|ჯეო]] ([[User talk:ჯეო|discuss]] • [[Special:Contributions/ჯეო|contribs]]) 17:23, 1 March 2019 (UTC)

:{{at|ჯეო}} See https://beta.wikiversity.org/wiki/Main_Page. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:00, 1 March 2019 (UTC)

დიდი მადლობა (Didi Madloba-Thank You)!--[[User:ჯეო|ჯეო]] ([[User talk:ჯეო|discuss]] • [[Special:Contributions/ჯეო|contribs]]) 08:44, 2 March 2019 (UTC)

::Please see [[betawikiversity:Category:KA]]. That is the appropriate place to create learning pages in this language. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 14:11, 10 March 2019 (UTC)

== new langueages ==

we should admit crosing of languajes to have a better understanding--[[Special:Contributions/201.208.239.198|201.208.239.198]] ([[User talk:201.208.239.198|discuss]]) 19:34, 25 July 2019 (UTC)

:This is the English Wikiversity. See [[:es:Portada|Wikiversidad]] for Wikiversity in Spanish. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 22:39, 25 July 2019 (UTC)

== How to change an username? ==

How to change an username? --[[User:Josephina Phoebe White|Josephina Phoebe White]] ([[User talk:Josephina Phoebe White|discuss]] • [[Special:Contributions/Josephina Phoebe White|contribs]]) 07:27, 28 August 2019 (UTC)
*{{ping|Josephina Phoebe White}} You can request at [[Special:GlobalRenameRequest]] --[[User:94rain|94rain]] ([[User talk:94rain|discuss]] • [[Special:Contributions/94rain|contribs]]) 07:29, 28 August 2019 (UTC)
Thanks. --[[User:Josephina Phoebe White|Josephina Phoebe White]] ([[User talk:Josephina Phoebe White|discuss]] • [[Special:Contributions/Josephina Phoebe White|contribs]]) 07:45, 28 August 2019 (UTC)

==Religious user names allowed in Wikiversity?==

https://en.m.wikiversity.org/wiki/Wikiversity:Username

Names of religious figures such as &quot;God&quot;, &quot;Jehovah&quot;,&quot;Buddha&quot;,&quot;Jainism&quot;,&quot;Bonadea&quot;,Hinduism or &quot;Allah&quot;, which user names prohibited

Please answer for my question. This Wikiversity user name policy still alive? Religious user names are prohibited? 

:It isn't a policy, but it's a guideline for people who are wanting to register an account are recommended to follow (as per the page, which could be changed with community consensus). I see no reason for this statement to be &quot;dead&quot;. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 00:15, 2 September 2019 (UTC)
::: Yes: Religious user names are under hedding &quot;Inflammatory usernames&quot;, will be blocked and not allowed.

== LinkedIn ==

I insist that a Wikiversity page should be added on LinkedIn. Wikimedia has its LinkedIn page; Wikipedia, too. But not Wikiversity. I tried to show my Swedish studies but could not choose Wikiversity as the Institution. Why not? Even when it is not a &quot;granting degree&quot; Institution, is is still an Institution, right? When I contacted LinkedIn about this, they sent me the link so that I can create myself the Wikiversity page. But then there is box I must tick: &quot; I confirm I am an approved authority of this Institution to create this page&quot;, which is not the case. But I think there are many Wikiversity experts on here that woud qualify as Wikiversity Linkedin page creators. I can create the page if someone here approves, but I would need some info: # of employees, etc. --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 23:34, 18 January 2020 (UTC)

:The information would go here [https://www.linkedin.com/company/setup/new/ Wikiversity institution] but it probably should have a bureaucrat or someone from the WMF tick &quot;I verify that I am an authorized representative of this organization and have the right to act on its behalf in the creation and management of this page. The organization and I agree to the additional terms for Pages.&quot; The number of employees (volunteers is not an option but we are unpaid) for our Wikiversity I guess could be the number of active users 201-500. The current logo is File:Wikiversity logo 2017.svg. The website can be https://en.wikiversity.org/wiki/Wikiversity:Main_Page.--[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 00:16, 19 January 2020 (UTC)

{{At|Leonardo T. Cardillo}} Wikiversity is a community. None of us gets to insist that anything happen on behalf of the community unless there is consensus to do so. This requires a discussion in the [[Wikiversity:Colloquium]] and a vote for support or lack thereof. Because this request involves an outside organization, it may also require support from the WMF.

I have some concerns at this point that your passion regarding this issue far exceeds your demonstrated commitment to either Wikiversity or the wider Wikimedia community. It might be better to let this rest for a bit and learn more about how Wikiversity functions before insisting that this be discussed. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 03:29, 19 January 2020 (UTC)

:{{At|Dave Braunschweig}}: I apologize for the use of the word &quot;insist&quot;, I have taken note to not use it anymore here to avoid distractions from the main topic of conversation. Also, I do not like you judge how much my passions should go against my level of contributions. With that being said, and for my personal learning on this environment, can someone please guide me on the very first step I should take to have a Wikiversity page created on LinkedIn? I think you mentioned something like a &quot;poll&quot;, how do I do that? --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 04:38, 19 January 2020 (UTC)

::{{At|Leonardo T. Cardillo}} I have already guided you on the next step to take. Please read my response carefully. Then slow down and learn more about Wikiversity. We often have people come in with high passions and quick fixes that Wikiversity must make in order to improve. They're typically gone within a month and we're left having to clean up after them. That's not to suggest that this is or isn't a good idea. It is simply to point out that this is a community. You must first learn to work with the community before you try to change it. We look forward to working with you as you figure this out. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 15:31, 19 January 2020 (UTC)

:::{{At|Dave Braunschweig}} Thanks so much for your inputs. I have created this: https://en.wikiversity.org/wiki/Wikiversity:Colloquium#LinkedIn. Please indicate if that is the next step that was intended to be created. Also, please guide on the following ones. Best regards, --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 16:27, 19 January 2020 (UTC)

== Add New Language ==

Why not bn.wikiversity?  But there is Hindi!  Make it, please.  I am ready to cooperate if needed. [[User:Hirok Raja|Hirok Raja]] ([[User talk:Hirok Raja|discuss]] • [[Special:Contributions/Hirok Raja|contribs]]) 03:07, 1 August 2020 (UTC)

:[[User:Hirok Raja|Hirok Raja]]: please see [[:betawikiversity:|Wikiversity Beta]]. &amp;mdash;Hasley&amp;nbsp;[[user talk:Hasley|&lt;span style=&quot;color: #0645AD; vertical-align: super; font-size: smaller;&quot;&gt;talk&lt;/span&gt;]] 13:04, 1 August 2020 (UTC)

:{{At|Hirok Raja}} Also see [[meta:Wikiversity]]. We are the English Wikiversity. We have no role in setting up new Wikiversity languages. When bn.wikiversity is added, please let us know, and we will add it to our main page. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:59, 1 August 2020 (UTC)

== I'm learning Turkish🤩 ==

Hi(to the person reading this)! I'm learning Turkish and I would like someone(native Turkish speaker) to teach how to pronounce Turkish. I do know some words,alphabets and number☺️ and I'm still learning and I hope someone is willing to help me🥺.

@JinahJady! [[User:JanehJody|JanehJody]] ([[User talk:JanehJody|discuss]] • [[Special:Contributions/JanehJody|contribs]]) 18:14, 4 February 2021 (UTC)

:Hi. Welcome to Wikiversity! Please see our [[Turkish|resources relating to the study of the Turkish language]]. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:41, 4 February 2021 (UTC)
::Hi,@[[User:JanehJody|JanehJody]] can i help you ::) [[User:MexmetW|MexmetW]] ([[User talk:MexmetW|discuss]] • [[Special:Contributions/MexmetW|contribs]]) 07:47, 28 September 2022 (UTC)
:Hi,@[[User:JanehJody|JanehJody]] I would love to help you to learning turkish :) [[Special:Contributions/85.105.185.109|85.105.185.109]] ([[User talk:85.105.185.109|discuss]]) 07:31, 28 September 2022 (UTC)

== Is it Wikipedia remodeled or a copy of wikipedia? ==

I am confused--[[User:Noukden|Noukden]] ([[User talk:Noukden|discuss]] • [[Special:Contributions/Noukden|contribs]]) 20:45, 24 May 2021 (UTC)

:{{At|Noukden}} None of the above. See [[What is Wikiversity?]] and [[What Wikiversity is not]]. Wikiversity is learning projects. Link to Wikipedia rather than duplicating it and then add hands-on activities so users can learn by doing. See [[IT Fundamentals]] for one approach. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:15, 25 May 2021 (UTC)

== Action in the earliest? ==

I want to know much more of all action that happend in the earliest centuries. [[User:Dilbkhay|Dilbkhay]] ([[User talk:Dilbkhay|discuss]] • [[Special:Contributions/Dilbkhay|contribs]]) 14:57, 21 August 2021 (UTC)

:Depending upon what you mean by &quot;earliest&quot;, have a look at [[Paleanthropology]] or [[Philosophy/Sciences]]. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 21:07, 20 September 2021 (UTC)

== Biology ==

What are the basic principles of ecology [[User:Aludriyo Dominic|Aludriyo Dominic]] ([[User talk:Aludriyo Dominic|discuss]] • [[Special:Contributions/Aludriyo Dominic|contribs]]) 18:25, 25 January 2022 (UTC)

:{{At|Aludriyo Dominic}} Welcome! See [[Wikipedia:Ecology]]. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:17, 26 January 2022 (UTC)
:{{ping|Aludriyo Dominic}} I invite you to read [[User:Atcovi/Science/Ecology]] if you're interested in learning about the basics of Ecology. Also check out the wikipedia link above and [[:Category:Ecology|this category]]. Thanks and weclome! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 03:44, 26 January 2022 (UTC)

I will try to study [[User:Aludriyo Dominic|Aludriyo Dominic]] ([[User talk:Aludriyo Dominic|discuss]] • [[Special:Contributions/Aludriyo Dominic|contribs]]) 05:41, 28 January 2022 (UTC)

== Physics ==

Physics Can Be defined as A Pure Science Subject That deals with the Measurement Of Matter In relation to energy. --{{Unsigned|Oyeyemi Abdul-warith|29 January 2022}}

: Welcome to Wikiversity! Here is a landing page that may be helpful: [[Physics]]. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 16:42, 29 January 2022 (UTC)

== Popularize ==

Can someone popularize California or the State of Washington on the Main Page? [[Special:Contributions/2604:3D08:6286:7500:B441:2710:77A4:1304|2604:3D08:6286:7500:B441:2710:77A4:1304]] ([[User talk:2604:3D08:6286:7500:B441:2710:77A4:1304|discuss]]) 03:33, 26 June 2022 (UTC)

:No, sorry, promotion isn't part of the [[Wikiversity:Mission]]. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 12:06, 26 June 2022 (UTC)

== [[w:Armistice of WWI|Armistice of WWI]], [[w:Paris Peace Conference|Paris Peace Conference]] and Aftermath ==

The best time to feature this on the main page was last week or yesterday;  the second best time is today.

* [[w:Template:First_World_War_treaties]]  (this template should get transcluded or copied to wikiversity, since this doesn't work: {{w:First_World_War_treaties}} although I wish it would)
* [[Wikiversity:Colloquium#Proclaiming_Armistice_of_WWI_Remembrance_and_Veterans_Day_for_11th_Nov]] our course on WWI is woefully inadequate, but this is a good time to start improving it!
[[User:Jaredscribe|Jaredscribe]] ([[User talk:Jaredscribe|discuss]] • [[Special:Contributions/Jaredscribe|contribs]]) 10:22, 12 November 2023 (UTC)

== Can you please add isiZulu plz ==

Because all othere languages her so i can umderstand batter  [[User:Lucky Shabalala|Lucky Shabalala]] ([[User talk:Lucky Shabalala|discuss]] • [[Special:Contributions/Lucky Shabalala|contribs]]) 06:06, 30 April 2025 (UTC)

:Add it how? Add more resources to learn the language? I think that would be fantastic, but it's very labor-intensive and I doubt anyone here has the competence to add that kind of material. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 08:40, 30 April 2025 (UTC)

== banner ==

says set learning free, propare grammer would be Start learning for free [[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 20:21, 3 February 2026 (UTC)

:I'm a native American English speaker and this banner is grammatical. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 08:52, 4 February 2026 (UTC)
::That’s not the problem. I’m wondering if we should more clearly emphasize what Wikiversity is on this banner. Idk maybe it’s fine as it is I would just like it to be clearer[[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 16:15, 4 February 2026 (UTC)
:::nevermind i just got the banner thought it was supposed to say start learning free, but its actually set learning free(like release learning) [[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 16:12, 6 February 2026 (UTC)</text>
      <sha1>p9vnqdyeawhkhw1jz0zp7l65lh9pdcq</sha1>
    </revision>
  </page>
  <page>
    <title>Wikiversity:Colloquium</title>
    <ns>4</ns>
    <id>28</id>
    <revision>
      <id>2815780</id>
      <parentid>2815590</parentid>
      <timestamp>2026-06-15T04:00:25Z</timestamp>
      <contributor>
        <username>Pine</username>
        <id>411839</id>
      </contributor>
      <comment>/* June 2026 Wikimedia Café meetups regarding the English Wikipedia Editor Reflections project */ new section</comment>
      <origin>2815780</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="40118" sha1="1q96mvbmg53b7dwuakqnybf8op8bmqj" xml:space="preserve">{{Wikiversity:Colloquium/Header}}
&lt;!-- MESSAGES GO BELOW --&gt;

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)
:::+1 Jtneill. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 12:59, 19 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
::A few days shy of 30, it seems obvious that this is not going to pass. So I '''withdraw''' as presumptively '''failed'''. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:14, 9 June 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)
*{{contra}} This seems like a proposal to continue the mission of WikiNews, but not a proposal specifically to improve Wikiversity. I concur with Juandev's comments. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 20:29, 30 May 2026 (UTC)
* {{oppose}} per above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:05, 1 June 2026 (UTC)
*{{oppose}} Wikiversity isn’t Wikinews and it also isn’t a dumping ground for anything not covered by other projects. It was already suggested, rather bafflingly, that Wikinews parasitize Wikipedia as a host. If it were allowed to freeload off of Wikiversity it would simply promote a view I and likely many others have— that Wikiversity (as it currently exists) has no standards and mostly just exists to host subpar content that wouldn’t be tolerated on any other Wikimedia site. Wikinews needs a new, non-Wikimedia host, and Wikiversity needs to get its act together by enforcing a minimum scope and standard for what it allows. --[[User:Dronebogus|Dronebogus]] ([[User talk:Dronebogus|discuss]] • [[Special:Contributions/Dronebogus|contribs]]) 01:16, 4 June 2026 (UTC)
* {{oppose}} per above. Wikiversity&lt;math&gt;\not=&lt;/math&gt; Wikinews - not a good idea to mix the scope of projects. --[[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 12:03, 8 June 2026 (UTC)
* {{abstain}} I will abstain since I'm not an active Wikiversity contributor. But I just feel like Wikinews had a very clear and specific goal of providing news, and Wikiversity is just a different project with different goals. For me, it would be odd to rehost Wikinews here. But please do not count my vote, this is only a comment. --[[User:Antimundo|Antimundo]] ([[User talk:Antimundo|discuss]] • [[Special:Contributions/Antimundo|contribs]]) 13:19, 6 June 2026 (UTC)
* {{oppose}} Although I think it's a pity that Wikinews is closed. --[[User:Dick Bos|Dick Bos]] ([[User talk:Dick Bos|discuss]] • [[Special:Contributions/Dick Bos|contribs]]) 19:06, 8 June 2026 (UTC)
*{{support}} In 2018 I initiated [[:Category:Videoconferences on media and democracy]] as a platform for disseminating public affairs events. In 2021 I officially initiated a podcast series on &quot;Media &amp; Democracy&quot; syndicated for the [[w:List of Pacifica Radio stations and affiliates|Pacifica radio network]]. In 2024 I converted it from irregular to fortnightly. I think this is all educational and supports the Wikiversity education mission, and I think that &quot;rehost Wikinews here&quot; would be appropriate. (I had some experience with Wikinews a few years ago. I felt it was too tightly controlled: Article submissions went stale, because I could not get official permission to publish and I could not get the information needed to understand what I was supposed to do to obtain the official permission. I would be opposed to rehosting Wikinews here if the policy similarly made it unreasonably difficult for volunteer contributor to get the information needed to meet the journalistic standards imposed by the overworked editors.) {{unsigned|DavidMCEddy}}

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)
*Note: I am not a regular here, and just visit Wikiversity for the WikiJournal project. Challenges of Wikinews included that it required timely reporting and fact-checking processes which differed greatly from the well-established ones in Wikipedia. Here in Wikiversity, there is the WikiJournal project, and that can take some some forms of journalism, just not breaking news reporting. I am in favor of salvaging parts of Wikinews if helpful. Could it, would it be feasible to adapt Wikijournal to accept some forms of news journalism, but just not the timed news reporting? For example, WikiJournal already is doing conference proceedings, and could likely do related event reports even months after the event ended. It could probably accept long-form investigative reporting, which is a sort of news that is not breaking news. I am not sure what the possibilities are, but I would prefer to build up systems that already work rather than import systems which had problems elsewhere. Thanks. [[User:Bluerasberry|&lt;span style=&quot;background:#cedff2;color:#11e&quot;&gt;''' Blue Rasberry '''&lt;/span&gt;]][[User talk:Bluerasberry|&lt;span style=&quot;cursor:help&quot;&gt;&lt;span style=&quot;background:#cedff2;color:#11e&quot;&gt;(talk)&lt;/span&gt;&lt;/span&gt;]] 19:17, 22 May 2026 (UTC)
*:I agree that there are certain kinds of journalism that are perfectly valid and not time-bound like breaking news reporting, so that won't suffer from the issues noted before. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:15, 22 May 2026 (UTC)
*::@[[User:Bluerasberry|Bluerasberry]] WikiJournal is not interested in taking on news journalism. WikiJournal is publishing conference proceedings at the request of some Wikimedian educators, and conference proceedings is what a &quot;regular&quot; journal publishes. News journalism is quite different from this, and if WikiJournal starts to deviate towards publishing news journalism, it will create barrier towards future initiatives like being indexed in Medline or Web of Science, and may risk being delisted from Scopus. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 22:43, 5 June 2026 (UTC)
*:::Thats a good point. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:09, 9 June 2026 (UTC)

== Create an autopatrolled user group? ==

{{tracked|T428269|resolved}}
I would like to propose creating the user group &lt;code&gt;autopatrolled&lt;/code&gt; (autopatrolled user), in which for non-curators and non-custodians, their page creations and file uploads would be automatically marked as patrolled by the MediaWiki software. Custodians may grant the user group, at their discretion, to users who create good quality pages that do not need frequent patrolling.

On a side note, the term {{tq|autopatroller}} would be used, but because we don't have non-curator/custodian patrollers (as we rely on curators and custodians to patrol), I suggest on using the term {{tq|autopatrolled user}}. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:31, 29 May 2026 (UTC)

:'''Support''' re: the name, I don't really understand the reasoning, so I am '''neutral''' on that. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:45, 29 May 2026 (UTC)
:: Regarding the name, this is because as we don't have the patroller user group, we rely on curators and custodians to patrol new pages and file uploads. Does that make sense? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:39, 29 May 2026 (UTC)
:::Not really, but I don't think it's the most important thing. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:42, 29 May 2026 (UTC)
:::: We'll decide on the name later. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 01:48, 30 May 2026 (UTC)
:::::Oh, please don't let me stand in the way. I'm just not very smart, so don't hold up a matter on my account. I didn't want to derail the proposal, which is a fine and sensible one. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:16, 30 May 2026 (UTC)
: '''Support''' - sounds like a good idea
:* Suggest adding a draft section about this group to [[Wikiversity:Patrolling]]. There is a statement in the Introduction of the page that I'm not sure if its correct and at least could be improved: &quot;Wikiversity also uses an autopatrol right, meaning trusted users' contributions are automatically marked as checked so patrollers can focus on reviewing newer or anonymous editors.&quot;
:* Regarding autopatroller vs autropatrolled user, what terms are used on similar WMF wiki projects?
: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:28, 30 May 2026 (UTC)
::# I would create a starting page about the user groups, with experienced editors expanding the page. A summarized part of that page would also be added to [[Wikiversity:Patrolling]].
::# For a similar example, English Wikipedia uses the term {{tq|Autopatrolled}}, just that term only.
:: [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:22, 30 May 2026 (UTC)
: @[[User:Jtneill|Jtneill]] and @[[User:Koavf|Koavf]]: the autopatroller user group has been implemented here. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 8 June 2026 (UTC)
::Thanks. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:13, 9 June 2026 (UTC)

== How much of Wikiversity’s content is LLM slop? ==

Because it seems like a non-trivial amount, along with AI slop images as well. Is there some kind of AI cleanup project established yet? [[User:Dronebogus|Dronebogus]] ([[User talk:Dronebogus|discuss]] • [[Special:Contributions/Dronebogus|contribs]]) 01:20, 4 June 2026 (UTC)

:We have discussed AI but I don't know of any explicit initiative to find and delete AI-generated noise. Individual modules have been deleted for having been made by AI. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 08:50, 4 June 2026 (UTC)
:Recently agreed [[Wikiversity:Artificial intelligence|policy]] welcome users to tag AI generated pages. Me personally I am not against the use of AI. What is the difference in abstract schematic image created by a human and the same by an AI. If the users does not have finances to pay digital artest and you dont want to let them use AI, would you pay the artest for them? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:07, 8 June 2026 (UTC)
::Wikimedia has a lot of ''volunteer'' artists who can illustrate if asked. [[User:Dronebogus|Dronebogus]] ([[User talk:Dronebogus|discuss]] • [[Special:Contributions/Dronebogus|contribs]]) 08:11, 9 June 2026 (UTC)
:::Interesting! That's good to know. Where can we find the volunteer artists for illustrating? [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 20:11, 9 June 2026 (UTC)
::::Wikimedia commons has [[commons:Commons:Graphic Lab/Illustration workshop]] [[User:Dronebogus|Dronebogus]] ([[User talk:Dronebogus|discuss]] • [[Special:Contributions/Dronebogus|contribs]]) 02:18, 10 June 2026 (UTC)

== Draft inactivity policy ==

I created [[Wikiversity:Inactivity policy]] as a start. Any experienced Wikiversity user may feel free to expand it. This is also one-to-two step(s) towards opting out of the [[m:Admin activity review|AAR process]].

However, I made a bold change to reduce the response timeframe from one month to two weeks. In addition, should we reduce the inactivity timeframe to one year? For the latter, most projects use that timeframe and I suggested this for consistency. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:57, 4 June 2026 (UTC)

:I support those suggestions. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:55, 4 June 2026 (UTC)
: Juandev has posted some comments on the [[Wikiversity talk:Inactivity policy|talk page]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:30, 12 June 2026 (UTC)

== Proposed user group and/or possible policy changes ==

I want to discuss about user group and possible policy changes.

# First, interface administrators. I don't think we should allow interface administrators to remove their permission from their own account, since we have multiple active bureaucrats and we can ask them to remove the permission when done, or for them to add a temporary grant. This is according to the [[Wikiversity:IA|current IA policy]]. I also left [[Wikiversity talk:Interface administrators#My thoughts about this user group|my thoughts on the relevant talk page]].
# Second, curators. Given that curators have some sensitive custodian rights (such as &lt;code&gt;delete&lt;/code&gt; [but not &lt;code&gt;undelete&lt;/code&gt; or similar rights that allow viewing deleted content, unless the curatorship process is RFA-like] and &lt;code&gt;protect&lt;/code&gt;), it would probably make more sense only for bureaucrats to grant and remove it, on par with them granting (but not removing) custodian permissions.
# Third, about probationary custodians. [[Wikiversity:Probationary custodians]] is currently marked as historical, and the process might still exist on [[Wikiversity:Custodianship]]. Therefore, to maintain consistency with [[Wikiversity:Curatorship#How does one become a curator?]], I propose that we repeal the probationary custodianship process and change it more or less to align with the curatorship process, effectively making probationary custodians permanent ones. However, custodian mentors would still be retained.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:55, 5 June 2026 (UTC)

:#Yes, I agree.
:#Thats a good point, but I dont know. At least I dont think its a good idea that both groups i.e. crats and custodiants can do that, it may create chaos.
:#Another good point. It seems to me that the current situation is somewhat unclear and should be clarified. I understand the original status of [[Wikiversity:Probationary custodians|Probationary custodians]] as a historicall and invalid, but at the same time I consider myself a probationary custodian, because on the Wikiversity:Custodianship page in the ''[[Wikiversity:Custodianship#How does one become a custodian?|How does one become a custodian?]]'' section it says, I quote, ''&quot;II ...then you will be approved as a probationary custodian for a period of at least four weeks&quot;''.
:::Mentors should definitely be kept, but for certain applicants the probation and mentorship should be abolished. For example, if someone was an active custodian for 5 years, then loses their rights or gives them up for a year and then wants to resume their custodial activities, there is no reason for them to undergo a training period. It burdens both the mentors and the community with double voting. The only exception could be a situation where policies or tools for custodians change significantly during that year, or the candidate wants to.
:[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 06:08, 9 June 2026 (UTC)

== New user what do I do here ==
I love wikipedia and the wikiversity project seems super interesting. However I know very little about wikiversity and would like to know how i can best contribute to the project. Also if there are forums or discord or reddit that would be very helpful.
(One last thing is it normal that my userboxes don't work here) {{unsigned|AUBSTRAWBS}}
:Hey {{ping|AUBSTRAWBS}} Welcome to Wikiversity! I've left a welcome message on your talk page so that should provide you a plethora of useful links for you to look at so you can familiarize yourself with the project. Also, feel free to create the userboxes you need. Wikiversity doesn't have as many userboxes as Wikipedia. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:45, 8 June 2026 (UTC)

:Thank you very much :) hope to contribute a lot.  [[User:AUBSTRAWBS|AUBSTRAWBS]] ([[User talk:AUBSTRAWBS|discuss]] • [[Special:Contributions/AUBSTRAWBS|contribs]]) 21:50, 8 June 2026 (UTC)

== Towards an Ethics policy ==

In connection with the [[Wikiversity:Community Review/Removal of Wikidebates|discussion of Wikidebates]], I said that it would be good to establish a policy on ethics, or rather a boundary between ethical and unethical content, so that we don't have to discuss individual cases. In addition, today we also have some global policies that prohibit, for example, attacks on members of the Wikimedia movement or undermining other projects.

However, at the very beginning, I would start by collecting your opinions. What content or what research should not be allowed on Wikiversity? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 05:52, 9 June 2026 (UTC)

:One ethical issue that I think should be non-controversial is related to good faith in the learning modules. So, learning materials should not be hoaxes or encourage behavior or methods that don't work or that misrepresent the facts or the likelihood of something occurring, etc. and authors should also not plagiarize or misrepresent authorship, etc. That was quite a run-on, but I hope that others can tease out what I mean here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:39, 9 June 2026 (UTC)
::I look at it from a practical perspective. We can give that to the policy, but I see the problem in that we are not able to check it except plagiarism.
::Plagiarism can be partially detected during patrolling. I see a new text, I put part of it in Google and I check if it is copied from the web. It is a problem with copying from books or other offline sources, but sometimes it happens that someone finds out that something is copied from somewhere and it can be deleted.
::The biggest issue we have here is that we are missing Wikipedia's control mechanism: references. Only some types of resources on Wikiversity require references. In-line references are not often used in courses, exercises, lectures, etc. We are thus deprived of one of the excellent control mechanisms and the only option is for the increase in the number of members with various qualifications to check it for their colleagues. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:59, 9 June 2026 (UTC)
:::Having a policy and enforcing that policy are indeed two different things. If we are only concerned with issues that we can definitively enforce, then that will definitely change this conversation. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 08:06, 9 June 2026 (UTC)
::::ok [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:55, 13 June 2026 (UTC)
:AI generated content should not be allowed as it is inherently plagiarism. [[User:Dronebogus|Dronebogus]] ([[User talk:Dronebogus|discuss]] • [[Special:Contributions/Dronebogus|contribs]]) 08:14, 9 June 2026 (UTC)
::And if the user mention it was generated by an AI? Note that there is something called as public domain, that is the author wave its rights. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:53, 9 June 2026 (UTC)
:::Plagiarism isn’t copyright violation. Crediting the AI is not crediting the authors the AI stole from without credit. [[User:Dronebogus|Dronebogus]] ([[User talk:Dronebogus|discuss]] • [[Special:Contributions/Dronebogus|contribs]]) 10:18, 9 June 2026 (UTC)
::::I see, now I understand your point. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 13 June 2026 (UTC)

== Deployment of Legal and Safety Contacts Link in the Footer of Your Wiki ==

Hello community,

The Wikimedia Foundation has provided [[foundation:Legal:Wikimedia Foundation Legal and Safety Contact Information|a single legal and safety contact page]], to be linked in the footer of your wiki, to ensure access to accurate legal information. This is a regulatory requirement.

We have already rolled out links to English, German, Italian, Spanish Wikipedias and other wikis and we will deploy to your wiki soon.

Please [[m:Wikimedia Foundation Legal and Safety Contacts FAQ|read more on the project page]] and leave any comments in this thread or on [[m:Talk:Wikimedia Foundation Legal and Safety Contacts FAQ|the talk page]]. –– [[User:STei (WMF)|STei (WMF)]] ([[User talk:STei (WMF)|discuss]] • [[Special:Contributions/STei (WMF)|contribs]]) 18:12, 9 June 2026 (UTC)

:Thanks for the notice. In case anyone is not clear, we cannot locally change the text at the footer, as it [[:mw:Manual:Footer|requires access to the server settings]]. If we locally needed to change it, we would have to file a ticket at [[:phab:]]. Since the above was sent by someone from the WMF, I think they are on it and it will be updated without any action from anyone here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:24, 9 June 2026 (UTC)

== Image not displaying ==

Can anyone work out why this image isn't displaying?&lt;br&gt;
[[Educational Media Awareness Campaign/Physics/POTD 10]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:45, 11 June 2026 (UTC)

:Not sure, but it was an issue with the file itself and either way, it should be (and I have since done this) replaced with the SVG [[:File:Telescope-schematic.svg]]. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 13:59, 11 June 2026 (UTC)

== New nomination template(s) ==

I created {{tlx|Nomination}} when someone requests curator or custodian permissions, which often at least require mentorship. On the other hand, I might create {{tlx|Nomination 2}}, in which the latter does not have a section about mentorship (often used for bureaucrat or interface administrator nominations). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:29, 12 June 2026 (UTC)

== June 2026 Wikimedia Café meetups regarding the English Wikipedia Editor Reflections project ==

&lt;div class=&quot;border-box&quot; style=&quot;background-color: var(--background-color-warning-subtle, #f8eaba); max-width: 875px; padding: 5px; border: 1px solid black; margin: 5px; color: var(--clr-dark)&quot;&gt;
&lt;div class=&quot;box&quot; style=&quot;float:left; padding-top: 10px; padding-right: 10px; padding-left: 10px; padding-bottom: 10px;&quot;&gt;[[File:Wikimedia Café logo in plain SVG format.svg|60px|alt=The logo for the Wikimedia Café]]&lt;/div&gt;
Hello! There will be two '''[https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9 Wikimedia Café]''' discussion opportunities during the last weekend of June. Both sessions will focus on the [https://en.wikipedia.org/wiki/Wikipedia:Editor_reflections English Wikipedia Editor Reflections project]. The featured guest in the Café will be [https://en.wikipedia.org/wiki/User:Clovermoss User:Clovermoss]. Participants may attend either or both sessions.

#'''27 June 2026 15:00 UTC''' ([https://zonestamp.toolforge.org/1782572400 timestamp converter]), at a time friendly to the Americas, Africa, and Europe
#'''28 June 2026 03:00 UTC''' ([https://zonestamp.toolforge.org/1782615600 timestamp converter]), at a time friendly to Asia and the Pacific

Please see the Café page for more information, including [https://meta.wikimedia.org/wiki/Wikimedia_Caf%C3%A9#How_to_attend_the_session how to register]!
&lt;br /&gt;
[[File:Buntstifte Eberhard Faber crop 64h.jpg|860px|alt=cropped image of colored pencils]]&lt;/div&gt;
&lt;span style=&quot;white-space:nowrap;&quot;&gt;[[User:Pine|&lt;span style=&quot;color:#01796f; text-shadow:#00BFFF 0 0 1.0em&quot;&gt;↠Pine&lt;/span&gt;]] [[User talk:Pine|&lt;span style=&quot;color:DeepSkyBlue&quot;&gt;(&lt;b style=&quot;color:#FFDF00;text-shadow:#FFDF00 0 0 1.0em&quot;&gt;✉&lt;/b&gt;)&lt;/span&gt;]]&lt;/span&gt; 04:00, 15 June 2026 (UTC)</text>
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  </page>
  <page>
    <title>Wikiversity:Requests for proofreading</title>
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      <contributor>
        <username>Howie2024</username>
        <id>2995240</id>
      </contributor>
      <comment>Request for proofreading.</comment>
      <origin>2815769</origin>
      <model>wikitext</model>
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      <text bytes="5819" sha1="m901y8chsok7z5c5bdsbtmhv8x8b0gy" xml:space="preserve">{{shortcut|WV:PROOF}}
This page coordinates efforts to proofread new pages and pages which have recently undergone a major rewrite. If you stumble across a page that could use proofreading, or if you finish creating/rewriting a page, you are strongly encouraged to list it here. Pages should not be listed here or tagged with proofreading templates until the content of the page is fully (or almost fully) complete; i.e., until they are in the &quot;rough draft&quot; phase. 

==How to list a page for proofreading==
First of all, tag the page with &lt;nowiki&gt;{{subst:proofread}}&lt;/nowiki&gt; - this will place the page in the category, [[:Category:Pages in need of proofreading]]. Then, list the page in the [[#New requests|New requests]] section using the following format:

&lt;pre&gt;
=== PAGENAME ===
* '''Page:''' [[PAGENAME]]
* '''Requested by:''' ~~~~
* '''Status:''' Not yet proofread.
* '''Comments:''' Any comments that may help proofreaders.
&lt;/pre&gt;

Once the page has been thoroughly proofread and all grammatical, typographical, and stylistic mistakes removed, the request will be moved to the [[#Completed requests|Completed requests]] section and the {{tl|proofread}} tag removed. Proofreaders may also leave a note on the page's talk page about which version was finally found to be without further need of proofreading.

== New requests ==
Please add new requests to the bottom of this section, and be sure to follow the above-specified format!

=== Example Page ===
* '''Page:''' [[Example Page]]
* '''Requested by:''' [[User:AmiDaniel|AmiDaniel]] 23:53, 26 November 2006 (UTC)
* '''Status:''' Not yet proofread.
* '''Comments:''' This is just an example of how to file a request.

=== School of Biology: Genetics ===
* '''Page:''' [[Topic: Genetics]]
* '''Requested by:''' --[[User:TheVividDream|TheVividDream]] 02:35, 17 December 2006 (UTC)
* '''Status:''' Not yet proofread.
* '''Comments:''' Please help proofread all new pages under the ''topics'' subheader: Gene Regulation in Prokaryotes, Gene Regulation in Eukaryotes, Genetics of Cancer, Drosophila Sex Determination, and Genetic Control in Drosophila Patterning.  Thanks a ton!

=== Japanese Roman Character Pronunciation Guide ===
* '''Page:''' [[Japanese Roman Character Pronunciation Guide]]
* '''Requested by:''' [[User:Balloonguy|Balloonguy]] 21:38, 1 March 2007 (UTC)
* '''Status:''' Not yet proofread.
* '''Comments:'''

=== Introduction to Programming/Variables part 2 ===
* '''Page:''' [[Introduction to Programming/Variables part 2]]
* '''Requested by:''' [[User:Dmclean|Dmclean]] 14:40, 2 March 2007 (UTC)
* '''Status:''' Not yet proofread.
* '''Comments:''' The course that this page is part of is intended for people with no programming experience. Please check that the material is explained in clear, simple, plain language.

=== Probability Dilation Theory ===
* '''Page:''' [[Probability Dilation Theory]]
* '''Requested by:''' [[User:Howie2024|Howie2024]] ([[User talk:Howie2024|discuss]] • [[Special:Contributions/Howie2024|contribs]]) 03:07, 15 June 2026 (UTC)
* '''Status:''' Not yet proofread.
* '''Comments:''' Requesting proofreading for grammar, formatting, mathematical notation, and Wikiversity style. The article presents an exploratory mathematical framework for iterative probability reweighting, entropy evolution, and dilation fields. Associated subpages are under development.


== Completed requests ==

=== Control Structures and Logical Expressions in VB6 ===
* '''Page:''' [[Control Structures and Logical Expressions in VB6]]
* '''Requested by:''' [[User:AmiDaniel|AmiDaniel]] 00:03, 27 November 2006 (UTC)
* '''Status:''' proofread by &lt;span style=&quot;border: 0px solid;&quot;&gt;[[User:Heltec|{{font|color=#FFFFFF|face=&quot;Comic Sans MS&quot;|size=x-small|background= #008003|'''&amp;nbsp;Heltec&amp;nbsp;'''}}]][[User talk:Heltec|{{font|color=#001D000|face=&quot;Comic Sans MS&quot;|size=x-small|background=#FFFFFF|'''&amp;nbsp;talk&amp;nbsp;'''}}]]&lt;/span&gt; and [[user:HappyCamper|HappyCamper]]
* '''Comments:''' Brand new page; it may have many typos and nuiances I haven't noticed. Any help proofreading would be appreciated.

=== Introduction to Programming/Variables ===
* '''Page:''' [[Introduction to Programming/Variables]]
* '''Requested by:''' [[User:Dmclean|Dmclean]] 02:04, 8 February 2007 (UTC)
* '''Status:''' Seems alright to me. Not perfect, but beyond the proofreading stage at least. [[User:AmiDaniel|AmiDaniel]] ([[User talk:AmiDaniel|talk]]) 18:39, 1 March 2007 (UTC)
* '''Comments:''' The course that this page is part of is intended for people with no programming experience. Please check that the material is explained in clear, simple, plain language.

=== Computing in Japanese ===
* '''Page:''' [[Computing in Japanese]]
* '''Requested by:''' [[User:Balloonguy|Balloonguy]] 00:38, 9 January 2007 (UTC)
* '''Status:''' Looks good. [[User:AmiDaniel|AmiDaniel]] ([[User talk:AmiDaniel|talk]]) 18:42, 1 March 2007 (UTC)
* '''Comments:''' Also check the test.

== Participants ==
If you plan to be an active participant in proofreading new pages, please sign your name here.

# [[User:AmiDaniel|AmiDaniel]] 23:53, 26 November 2006 (UTC)
# [[User:HappyCamper|HappyCamper]] 23:57, 26 November 2006 (UTC)
# [[User:J.Steinbock|J.Steinbock]] 00:46, 27 November 2006 (UTC)
# &lt;span style=&quot;border: 0px solid;&quot;&gt;[[User:Heltec|{{font|color=#FFFFFF|face=&quot;Comic Sans MS&quot;|size=x-small|background= #008003|'''&amp;nbsp;Heltec&amp;nbsp;'''}}]][[User talk:Heltec|{{font|color=#001D000|face=&quot;Comic Sans MS&quot;|size=x-small|background=#FFFFFF|'''&amp;nbsp;talk&amp;nbsp;'''}}]]&lt;/span&gt; 00:54, 27 November 2006 (UTC)
# [[User:Dark Mage|&lt;strong&gt;{{font|color=Black|Dark}}{{font|color=Red| Mage}}&lt;/strong&gt;]] 19:27, 9 September 2008 (UTC)
# [[User:Helloworld00|Helloworld00]] 01:55, 29 April 2009 (UTC)

== See also ==
*[[:Category:Pages in need of proofreading]]
*[[Wikiversity:Peer review]]</text>
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  <page>
    <title>Fluid Mechanics for MAP/Introduction</title>
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    <revision>
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      <parentid>2572791</parentid>
      <timestamp>2026-06-15T11:44:27Z</timestamp>
      <contributor>
        <username>CommonsDelinker</username>
        <id>9184</id>
      </contributor>
      <comment>Replacing Hurricane_Katrina_August_28_2005_NASA.jpg with [[File:Katrina_2005-08-28_1702Z.jpg]] (by [[:c:User:CommonsDelinker|CommonsDelinker]] because: [[:c:COM:FR|File renamed]]: Criterion 4 - conforms to other similar files' formats for storm images).</comment>
      <origin>2815792</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="28517" sha1="bm7ksdjvn8t1rj3cib2bws5hnykzfjb" xml:space="preserve">[[Fluid_mechanics_for_MAP|&gt;back to Chapters]]
==Definition of Fluid==

Fluid Mechanics is the study of fluids at rest (fluid statics) and in motion (fluid dynamics).

&lt;!-- TWO PICTURES at the center--&gt;
{| cellspacing=&quot;10&quot; cellpadding=&quot;10&quot; style=&quot;margin:0em 0em 1em 0em; width:100%&quot;
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[[File:Itaipu 171.jpg|300px|center|thumb|Fluid in motion: Itaipu Dam]]
|}


A fluid is defined as a substance that continually deforms (flows) under an applied
shear stress regardless of the magnitude of the applied stress. Whereas a solid can
resist an applied force by static deformation.


[[Wikipedia:Liquid|Liquids]], [[Wikipedia:Gas|gases]], [[Wikipedia:Plasma_(physics)|plasmas]] and, to some extent, plastic solids are accepted to be fluids. A perfect fluid offers no internal resistance to change in shape and, consequently,  they take on the shape of their containers. Liquids form a free surface (that is, a surface not created by their container) whereas gases and plasmas do not,  but, instead, they expand and occupy the entire volume of the container.


{| cellspacing=&quot;10&quot; cellpadding=&quot;10&quot; style=&quot;margin:0em 0em 1em 0em; width:100%&quot;
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[[Image:Deformation_solid_vs_fluid.png|400px|thumb|border|center|Deformation of a solid and a fluid exposed to an applied force]]
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| style=&quot;width:40%; vertical-align:top; border:1px white; background-color:white;&quot; |
[[Image:Imagen3.png|400px|thumb|border|center|Behavior of liquids, gases and plasmas in a container]]
|}

==Motivation for studying fluid mechanics==
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The importance of flow phenomena is  out of question. Natural phenomena or technological applications are completely or partially involves flow phenomena. It can be met in a diverse range of length of time scales. Atmospheric flows and blood flows are two examples for this diversity. As a tool making specie, humankind learned also how to utilize flow phenomena. Hence, those, who deal with flowing matter, should be better equipped with theoretical understanding and capability to use experimental and numerical investigation tools.
[[File:Airbus A380 blue sky.jpg|400px|thumb|left|Airbus A380]]
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[[File:Katrina 2005-08-28 1702Z.jpg|300px|thumb|Hurricane Katrina August 28 2005 NASA]]
|}

==Historical Background and Future Perspective==
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Fluid mechanics have played an important role in human life. Therefore, it also attracted many curious people. Even in the ancient Greek history, systematic theoretical works have been done. The devlopement of governing equations of fluid flow started already in the 16th century. In the 18th and 19th century, the conservation laws for mass, momentum and energy was already known in its most general form. In the 20th century, developments were in theoretical, experimental and recently numerical. In the theoretical field, mostly solutions of the governing equations for special cases were provided. Experimental methods have been developed to measure flow velocities and fluid properties. By the developement of computers , the numerical treatment of fluid mechanical problems opened new perspectives in research. It is the common blief that in the 21th century, the activities would be most intensive in the  development new experimental and numerical tools and application of those for developing new technologies. 

&lt;gallery&gt;
File:Pont_du_gard.jpg|[[Wikipedia:Aquaduct|Aquaduct (Pont Du Gard), 7th cent. BC]]
File:Trireme.jpg|[[Wikipedia:Trireme|Greek ship (Trireme), 7th cent. BC]]
File:Leonardo_helicopter.JPG|[[Wikipedia:Science_and_inventions_of_Leonardo_da_Vinci|Helicopter design of Leonardo da Vinci]]
&lt;/gallery&gt;

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[[Image:Historical_Background.png|400px|thumb|right|Historical perspective to the developments in the field of fluid mechanics&lt;ref&gt;Durst, F., &quot;Grundlagen der Strömungsmechanik: Eine Einführung in die Theorie der Strömungen von Fluiden&quot;, Springer,2008.&lt;/ref&gt; ]]
|}

==Basic components of Fluid Mechanics Research==
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Besides theoretical considerations, exepriments and simulations are heavily used in research. If possible, most productive and accurate approach is the combination of all three methods. However, sometimes environmental conditions can be so harsh for any experimental technique that only theoretical or numerical methods can be used. For example, it is very hard or almost impossible to obtain the velocity or temperature distribution in the die casting mold or in the crucible used for crystal growth, because of very high temperatures.
[[Image:Process_diagnostics.png|500px|thumb|center|Simulations for diagnosing crystal growth process.]]
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[[Image:Experiments_and_simulations_train.png|250px|thumb|center|Experimental and numerical investigations conducted on a fast train.]]
|}

==Viscosity of a Fluid==

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Force applied on a matter creates stresses on it. Stress is simply force per unit area:

{{center top}}&lt;math&gt; \displaystyle 
	\tau = \frac{F}{A}\left[\frac{N}{m^{2}}= Pa\right]
&lt;/math&gt;{{center bottom}}
Hence the unit of stress is &lt;math&gt; Pa &lt;/math&gt;. There can be normal and shear stresses in and on the matter.

Shear stress is proportional to the deformation rate of the matter, i.e. strain rate:
{{center top}}&lt;math&gt; \displaystyle \tau \propto \frac{\delta \theta}{\delta t}&lt;/math&gt;{{center bottom}}

{{center top}}&lt;math&gt; \displaystyle \tan{\delta\theta}= \frac{\delta u \delta t}{\delta y}&lt;/math&gt;{{center bottom}}  

&lt;math&gt; \displaystyle u&lt;/math&gt; is the deformation speed. For very small deformation angles
{{center top}}&lt;math&gt; \displaystyle 
	\delta\theta = \frac{\delta u \delta t}{\delta y} \ \rightarrow \ \frac{\delta\theta}{\delta t} = \frac{\delta u}{\delta y} \ \rightarrow \ \tau \propto \frac{\delta u}{\delta y} \ \rightarrow \ \tau = \mu \frac{\delta\theta}{\delta t} = \mu \frac{\delta u}{\delta y}
&lt;/math&gt;{{center bottom}}

&lt;math&gt; \displaystyle \mu&lt;/math&gt; is the dynamic viscosity of the fluid. 


For the same &lt;math&gt; \displaystyle \tau&lt;/math&gt; and fluid having higher viscosity &lt;math&gt; \displaystyle \mu&lt;/math&gt;, the deformation rate, i.e. velocity gradient is smaller.

Dynamic viscosity is a thermodynamic property of the material and it depends on temperature and pressure. In general, viscosity of liquids drop by increasing temperature, whereas that of gases increases. The viscosities of liquids and gases increase with increasing pressure.
{{center top}}&lt;math&gt; \displaystyle \mu=f\left(T,P\right)\left[Pa\cdot s\right]&lt;/math&gt;{{center bottom}}

Often dynamic viscosity is normalized by the density of the fluid and this quantity is called “kinematic viscosity”:
{{center top}}&lt;math&gt; \displaystyle \upsilon=\frac{\mu}{\rho}\left[\frac{m^{2}}{s}\right]&lt;/math&gt;{{center bottom}}

One can judge the dominance of inertial effects to viscous effects by using a dimensionless number, namely  Reynolds number: 
{{center top}}&lt;math&gt; \displaystyle 
	Re=\frac{\rho U_{c}l_{c}}{\mu}=\frac{U_{c} l_{c}}{\upsilon}
&lt;/math&gt;{{center bottom}}
&lt;math&gt; \displaystyle U_{c}&lt;/math&gt; and &lt;math&gt; \displaystyle l_{c}&lt;/math&gt; are characteristic velocity and length scales of the flow.
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[[Image:Deformation_of_a_fluid_element.png|500px|thumb|center|Deformation of a fluid element]]


[[Image:Low viscous fluid.gif|200px|thumb|left|Deformation of a low viscous fluid under the applied stress.]]
[[Image:High viscous fluid.gif|200px|thumb|right|Deformation of a high viscous fluid under the applied stress.]]
|}

==Elasticity, viscosity, solid- and liquid-like behavior, and plasticity==
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When one tries to deform a piece of material, some of the above properties appear depending on the amplitude and duration of the applied stress.

*'''''Long time application of weak stress'':''' '''Solids''' initially deform and then resist to deform. '''Fluids''' deform (flow) continuously.

*'''''Short time application of weak stress'':''' If deformation follows the stress, material is '''elastic!!!.''' If '''deformation rate''' follows the stress, material is '''viscous.''' 

*'''''Application of high stress'':''' After a certain stress (yield stress), some solids start to deform irreversibly. These are called '''plastic solids.'''  There are also '''yield stress fluids''', whose threshold stress is much lower than plastic solids.

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[[Image:Elasticity.png|200px|thumb|Stress and strain (deformation) relation for a solid substance]]
|}

==Deborah number==
A transition from a more resistant (elastic) to a less resistant behavior (viscous) has a relevant characteristic time scale: '''the relaxation time of the material'''. Correspondingly, the ratio of the relaxation time of a material to the timescale of a deformation is called '''Deborah number''' :

&lt;math&gt; \displaystyle  \displaystyle De = \frac{\text{characteristic relaxation time of material}} {\text{time scale of deformation}} &lt;/math&gt;

'''Small Deborah numbers'''  correspond to situations where the material has time to relax (and behaves in a viscous manner), while '''high Deborah numbers'''  correspond to situations where the material behaves rather elastically.
Water can show elastic behavior  when the time scale of deformation becomes very short. For example, when one tries to jump to water from a height more than 100 meters, water feels like a solid ground at the instant of collision ( do not try).
'''Corn starch and water mixture'''  (suspension) is a good example with which low and high De number effects can be shown.

==Rheological Material==
Fluids can be classified according to the relation between stress &lt;math&gt; \displaystyle \tau&lt;/math&gt; and deformation rate &lt;math&gt; \displaystyle du/dy&lt;/math&gt;.
The [[Wikipedia:Newtonian_fluid|Newtonian fluids]] show a linear relation
{{center top}}&lt;math&gt; \displaystyle \tau = \mu\frac{du}{dy}\Rightarrow \mu=\mu(T,P)&lt;/math&gt;{{center bottom}}

Fluids which do not follow the linear law between stress an the deformation rate are called [[Wikipedia:Non-Newtonian_fluid|non-newtonian]] and they are the subject of [[Wikipedia:Rheology|rheology]].  A [[Wikipedia:Dilatant|dilatant (shear-thickening)]] fluid increases resistance with increasing
applied stress. Alternately, a [[Wikipedia:Pseudoplastic|pseudoplastic (shear-thinning)]] fluid decreases resistance
with increasing stress. If the thinning effect is very strong, the fluid is termed plastic. 
The limiting case of a plastic substance is one which
requires a finite yield stress before it begins to flow. The linear-flow Bingham plastic
idealization is shown in the figure, but the flow behavior after yield may also be nonlinear. Examples
of a yielding fluid are toothpaste and ketchup, which will not flow out of the tube until a finite
stress is applied by squeezing. 

Some fluids show  decreasing [[Wikipedia:Thixotropy|(thixotropic)]] or  increasing resistance [[Wikipedia:Rheopecty|(rheopectic)]] in time for the same deformation rate. 
For example, pudding is a rheopectic fluid and some paints are thixotropic.

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[[Image:Rheological-fluids-1.png|400px|thumb|center|Types of different fluids regarding their stress-strain dependence]]
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[[Image:Rheological-fluids-2.png|300px|thumb|center|Types of different fluids regarding the change of the stress in time for constant a strain]]
|}

[[Image:comparison_bet_solid_and_liquid_01.svg|300px|thumb|center|Comparison between solids and fluids]]

==Continuum Assumption==
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In many technical applications, the distance between the molecules (mean free path) (&lt;math&gt; \displaystyle \lambda&lt;/math&gt;) are much larger than the molecular diameter.  For air, &lt;math&gt;  \lambda&lt;/math&gt; is around  &lt;math&gt; 5 \times 10^{-8}m&lt;/math&gt;.

The molecules are not fixed in a lattice but move about freely relative to each other. Thus fluid density, or mass per
unit volume, has no precise meaning because the number of molecules occupying a given volume continually changes.
If the selected unit volume &lt;math&gt; \displaystyle \delta V &lt;/math&gt; is smaller than the cube of the mean free path between the molecules, there will be large scatter in the determination of density, since the molecules move freely relative to each other, i.e. at one instant the number of molecules in the unit volume is not constant.  This effect becomes unimportant if the unit volume is large compared with, say, the cube of the molecular spacing, when the number of
molecules within the volume will remain nearly constant in spite of the enormous interchange
of particles across the boundaries. In other words, when &lt;math&gt; \displaystyle \delta V&lt;/math&gt; is selected such that the selected volume contains in average the number of molecules, the density converges to a level. The acceptable size of the  unit volume for many liquids and gases is about &lt;math&gt; \displaystyle 1\mu m^{3}&lt;/math&gt;. Over this value, the medium can be accepted as '''continuum''' , such that the variations in space and time can be accepted to be smooth and differential equations can be written to describe the fluid motion. If, however, the chosen unit volume is too large, there could be a noticeable variation within the selected volume owing to the non-uniform bulk distribution of molecules caused by temperature and/or pressure variations in the flow field.
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[[Image:Continuum_assumption_sketch.png|300px|thumb|center|Continuum assumption in a fluid flow]]
|}

==Pressure in a fluid==
Pressure is force per unit area and is a scalar quantity.

{{center top}}&lt;math&gt; \displaystyle 
p=\frac{F}{A}\left[Pa\right]\ ; \left(1 bar = 10^{5} Pa\right)
&lt;/math&gt;{{center bottom}}


In a  fluid at rest,  the tangential viscous forces are  absent and the only force between adjacent surfaces is normal to the surface. In a resting fluid there is only a normal stress (pressure). In other words, force caused by the pressure on a surface is normal to that surface.


[[Image:pressure_in_a_fluid.png|300px|thumb|right|Pressure forces on an infinitesimal fluid element]]

Balance in x-direction:

{{center top}}&lt;math&gt; \displaystyle \left(p_{1}\ ds\right)\ sin\theta - p_{3}\ dz = 0&lt;/math&gt;{{center bottom}}


{{center top}}&lt;math&gt; \displaystyle dz=ds\sin\theta\longrightarrow p_{1} = p_{3}&lt;/math&gt;{{center bottom}}


Balance in z-direction:

{{center top}}&lt;math&gt; \displaystyle -\left(p_{1}\ ds\right)\ cos\theta + p_{2}\ dx - \frac{1}{2}\rho g\ dx\ dz = 0&lt;/math&gt;{{center bottom}}


{{center top}}&lt;math&gt; \displaystyle ds\ cos\theta = dx\longrightarrow p_{2} - p_{1} - \frac{1}{2}\rho g\ dz = 0&lt;/math&gt;{{center bottom}}


For an infinitesimal prism, effect of gravity can be neglected.


{{center top}}&lt;math&gt; \displaystyle \rightarrow p_{1} = p_{2} = p_{3}&lt;/math&gt;{{center bottom}}

==Interface phenomena and surface tension==
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Surface tension phenomena occur at the interface of  one liquid and another liquid, gas or a solid wall. 
The cohesive forces between molecules down into a liquid are shared with all neighboring atoms. Those on the surface have no neighboring atoms above, and exhibit stronger attractive forces upon their nearest neighbors on the surface. This enhancement of the intermolecular attractive forces at the surface is called '''surface tension.''' 

[[Image:Interface_Phenomena_and_surface_tension.png|500px|thumb|center|Examples of interface and surface tension phenomena]]
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[[File:WassermoleküleInTröpfchen.svg|thumb|250px|center|Inter molecular attraction in the liquid and on the liquid surface]]
|}

If the interface is curved, a mechanical balance shows that there is a pressure difference across the interface, the pressure being higher on the concave side,
{{center top}}&lt;math&gt; \displaystyle 
\Delta\ p=\sigma\left(\frac{1}{R_{1}}+\frac{1}{R_{2}}\right)
&lt;/math&gt;{{center bottom}}

where &lt;math&gt; \displaystyle \sigma\left[\frac{N}{m}\right]&lt;/math&gt; is the '''surface tension coefficient.''' Surface tension coefficient is not a property of the liquid alone, but a property of the liquid's interface with another medium.

According to the above equation, in the soap bubble or in the droplet, inner pressure is higher than outer pressure.
This can also be shown by a force balance. In the droplet, the force balance in the vertical direction reads

{{center top}}&lt;math&gt; \displaystyle F_{net}=\sigma2\pi\!R - \left(p_{i} - p_{0}\right)\pi\!R^{2}=0&lt;/math&gt;{{center bottom}}


{{center top}}&lt;math&gt; \displaystyle \Delta\ p=\sigma\frac{2}{R}&lt;/math&gt;{{center bottom}}


Similarly, in the soap bubble the force balance becomes
{{center top}}&lt;math&gt; \displaystyle \Delta\ p=\sigma\left(\frac{1}{R}+\frac{1}{R}\right)=\sigma\frac{2}{R}&lt;/math&gt;{{center bottom}}


{{center top}}&lt;math&gt; \displaystyle F_{net}=2\sigma2\pi\!R - \left(p_{i}-p_{0}\right)\pi\!R^{2}=0&lt;/math&gt;{{center bottom}}


{{center top}}&lt;math&gt; \displaystyle \Delta\ p=\sigma\frac{4}{R}&lt;/math&gt;{{center bottom}}

Note that owing to the two interfaces in the soap bubble force due to surface tension is as double as that in the droplet.

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[[Image:Surface_tension_Example.png|400px|thumb|center|Force balance in the droplet]]
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[[Image:Surface_tension_Example_2.png|400px|thumb|center|Force balance in the bubble]]
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The contact angle is the angle between the liquid-solid and gas-liquid interfaces. It is calculated such that angle remains in the liquid. It is dependent on the adhesion forces between the liquid molecules and the solid wall. These forces are sensitive to the actual physicochemical conditions of the solid-liquid interface. 

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[[Image:contact_angle.png|400px|thumb|center|Definition of contact angle]]
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[[File:Wetting.svg|thumb|400px|center|Wetting]]
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==Saturation pressure and cavitation==
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Evaporation occurs at the liquid gas interface. When the vapor pressure of liquid is less than  the liquid's saturation pressure at the given liquid temperature, the evaporation and condensation occurs at the same time on the interface.At the liquid solid interface, at a given temperature, liquids starts to boil at saturation pressure.

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[[File:Evaporation_boiling.png|350px|center|thumb|Evaporation and boiling of liquid]]

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[[File:Boiling_cavitation.png|300px|center|thumb|Boiling and cavitation shown on the saturation temperature and pressure diagram of water]]
|}
Instead of increasing the temperature of the liquid, one can decrease the pressure of the liquid so that it starts to boil, or so to say '''cavitates'''.


One can meet cavitation in nature and in technical application. One known example is the cavitation damage on ship propellers. An interesting natural occurrence of cavitation was observed while the snapping shrimp hunts &lt;ref&gt;[http://stilton.tnw.utwente.nl/shrimp/ How Snapping Shrimp Snap (and flash)? ]&lt;/ref&gt;.  


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[[File:Cavitation Propeller Damage.JPG|450px|thumb|center|Cavitation Propeller Damage]]
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==Streamline, streakline, pathline and timeline==
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Four basic types of line patterns are used to visualize flows:
* A streamline is a line everywhere tangent to the velocity vector at a given instant.
* A pathline is the actual path traversed by a given fluid particle.
* A streakline is the locus of particles which have earlier passed through a prescribed point.
* A timeline is a set of fluid particles that form a line at a given instant.

In a steady flow streamlines, streaklines and pathlines are identical.
  
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[[File:Aeroakustik-Windkanal-Messhalle.JPG|300px|right|thumb|Flow visualization around a car done by smoke. The lines are streaklines.]]
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==Laminar and turbulent flows==
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Laminar flows are:
* smooth,
* the disturbances are damped via viscous effects,
* and they are in general deterministic.

In turbulent flows:
* flow and fluid variables show random fluctuations in time and space, i.e. the flow is stochastic
* there are eddies of velocity and length scales over a very wide range

Laminar to turbulent transition occurs when the disturbances in the flow can not be damped anymore by viscous forces. This happens when the inertia of the flow is increased and/or the flow configuration (boundaries, states of the fluid(s)) causes the generation and/or amplification of very small disturbances. As Reynolds  number (Re) is the ratio of the inertial forces to viscous forces, for different types of flows, over a critical Reynolds number, transition to turbulence takes place. Below a list of simple but still technically interesting flow cases and critical Reynolds numbers are listed:

* Pipe flow: &lt;math&gt; Re=\frac{U_b D_{pipe}}{\nu} &gt; 2200 &lt;/math&gt;
* Jet flow: &lt;math&gt; Re=\frac{U_b D_{jet}}{\nu} &gt; 1000 &lt;/math&gt;
* Flow over a flat plate: &lt;math&gt; Re=\frac{U_\infty \delta_l}{\nu} &gt; 950 &lt;/math&gt;

where &lt;math&gt; U_b &lt;/math&gt;, &lt;math&gt; U_ \infty &lt;/math&gt; are the bulk velocity of the fluid  or the velocity of fluid  approaching to the plate. &lt;math&gt; D_{pipe} &lt;/math&gt;, &lt;math&gt; D_{jet} &lt;/math&gt; and &lt;math&gt; l &lt;/math&gt; are the pipe diameter, jet diameter or the length of the plate. &lt;math&gt; \delta_l= 1.72 \sqrt{ \nu l / U_\infty }&lt;/math&gt; is the displacement thickness.


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[[File:jet_transition.png|300px|thumb|Laminar to turbulent transition of a submerged jet flow.]]
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==Compressibility==

Ideal Gas law (Equation of State)


&lt;math&gt;\displaystyle p = \rho RT &lt;/math&gt; :  Where R is the gas constant and T is the universal temperature.


&lt;math&gt;R_{air} = 286,9 \left[\frac{J}{kg}K\right]&lt;/math&gt;

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Density and volume change:

&lt;math&gt;\displaystyle \rho = \frac{m}{V}&lt;/math&gt;

&lt;math&gt;\displaystyle \frac{d\rho}{dV} = -\frac{m}{V^2} = -\frac{m}{V} \frac{1}{V} = -\rho \frac{1}{V}&lt;/math&gt;

&lt;math&gt;\displaystyle \frac{d\rho}{\rho} = -\frac{dV}{V}&lt;/math&gt;


The Bulk Modulus:


&lt;math&gt;\displaystyle E_{v} = - \frac{dp}{\frac{dV}{V}} = \frac{dp}{\frac{d\rho}{\rho}} \ [Pa] &lt;/math&gt;


Large values of Ev means that the fluid is relatively incompressible.


Under standard atmospheric conditions:


&lt;math&gt; E_{v} = 2.15 \times 10^{9} \ Pa = 21500\ bar\ &lt;/math&gt;  


for water and


&lt;math&gt; E_{v} = 1.42 \times 10^{5} \ Pa = 1.4\ bar\ &lt;/math&gt;  


for air. Therefore air is 15000 times more compressible than water.

Liquids can be accepted to be incompressible in many applications. Air can be compressible, especially when there are large changes of pressure in the flow.


&lt;math&gt;\frac{d\rho}{dt} = 0 &lt;/math&gt;  and  &lt;math&gt; \frac{d\rho}{dx_{i}} = 0 &lt;/math&gt; 


Where i = 1,2,3.

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[[File:Compressibility 01.svg|250px|center|thumb|Figure: Gas under pressure]]
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==Classification of flows==
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Following chart covers most of the flow phenomena, which might occur in a flow problem. When one deals with a flow problem, first task is to classify the flow. Correct classification helps to choose the correct and most efficient methods to deal with this problem. 
[[File:Classi.png|300px|thumb|center]]

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==References==
&lt;references/&gt;

[[Category:Fluid Mechanics for MAP]]</text>
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    <title>Physics Formulae/Quantum Mechanics Formulae</title>
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      <text bytes="15511" sha1="t1y7s6ba588ghxtpuqvmixylif4w7eb" xml:space="preserve">'''Lead Article: [[Tables of Physics Formulae]]'''


This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Quantum Mechanics.


The nature of Quantum Mechanics is formulations in terms of probabilities, operators, matrices, in terms of energy, momentum, and wave related quantites. There is little or no treatment of properties encountered on macroscopic scales such as force.

==Applied Quantities, Definitions==


Many of the quantities below are simply energies and electric potential differances.


{| class=&quot;wikitable&quot;
|-
! Quantity (Common Name/s) !! (Common) Symbol/s !! Defining Equation !! SI Unit !! Dimension
|-

|Threshold Frequency
||''f''&lt;sub&gt;0&lt;/sub&gt;
||&lt;math&gt; f_0 \,\!&lt;/math&gt;
|| Hz = s&lt;sup&gt;-1&lt;/sup&gt; 
|| [T]&lt;sup&gt;-1&lt;/sup&gt;
|- 

|Threshold Wavelength
||&lt;math&gt; \lambda_0 \,\!&lt;/math&gt;
||&lt;math&gt; \lambda_0 = \frac{c}{f_0} \,\!&lt;/math&gt;
|| m
|| [L]
|-


|Work Function
||&lt;math&gt; \phi, \Phi \,\!&lt;/math&gt;
||&lt;math&gt;\Phi = h f_0\,\!&lt;/math&gt;
||J
||[M] [L]&lt;sup&gt;2&lt;/sup&gt; [T]&lt;sup&gt;-2&lt;/sup&gt;
|-

|Stopping Potential
||''V''&lt;sub&gt;0&lt;/sub&gt;
||&lt;math&gt;V_0 = e \Phi_0 \,\!&lt;/math&gt;
||J
||[M] [L]&lt;sup&gt;2&lt;/sup&gt; [T]&lt;sup&gt;-2&lt;/sup&gt;
|-


|}

==Wave Particle Duality==


===Massless Particles, Photons===


{| class=&quot;wikitable&quot;
|-
|Planck–Einstein Equation
|&lt;math&gt;E = hf = \frac{hc}{\lambda}\,\!&lt;/math&gt;
|-

|Photon Momentum
|&lt;math&gt;p = \frac{hf}{c} = \frac{h}{\lambda}\,\!&lt;/math&gt;
|-

|}


===Massive Particles===


{| class=&quot;wikitable&quot;
|-

| De Broglie Wavelength
|&lt;math&gt;  p = \frac{h}{\lambda} = \hbar k \,\!&lt;/math&gt;
|-

|Heisenberg's Uncertainty 

Principle
|&lt;math&gt;\Delta x \Delta p_x \geqslant \frac{\hbar}{2} \,\!&lt;/math&gt;

&lt;math&gt;\Delta E \Delta t \geqslant \frac{\hbar}{2} \,\!&lt;/math&gt;
|-

|}


Typical effects which can only explained by Quantum Theory, and in part brought rise to Quantum Mechanics itself, are the following.


{| class=&quot;wikitable&quot;
|-
|'''Photoelectric Effect''':

Photons greater than threshold frequency incident on a metal surface 

causes (photo)electrons to be emmited from surface.


||&lt;math&gt;E_\mathrm{k\;\;\!\!max} = hf - \Phi\,\!&lt;/math&gt;
|-

|'''Compton Effect'''

Change in wavelength of photons from an X-Ray source depends only 

on scattering angle. 

||&lt;math&gt;\Delta \lambda = \frac{h}{2m} \left( 1 - \cos \theta \right )  \,\!&lt;/math&gt;
|-

|'''Moseley's Law'''

Frequency of most intense X-Ray Spectrum (K-α) line for an element, 

Atomic Number ''Z''.
||&lt;math&gt; f = \frac{c}{\lambda} = M_{K_\alpha} (Z - 1)^2 &lt;/math&gt; 

&lt;math&gt; M_{K_\alpha} = 2.47 \times 10^{15} &lt;/math&gt; Hz

|-

|'''Planck's Radiation Law'''

''I'' is ''spectral radiance'' (W m&lt;sup&gt;-2&lt;/sup&gt; sr&lt;sup&gt;-1&lt;/sup&gt; Hz&lt;sup&gt;-1&lt;/sup&gt; for frequency or W m&lt;sup&gt;-3&lt;/sup&gt; sr&lt;sup&gt;-1&lt;/sup&gt; for 

wavelength), not simply intensity (W m&lt;sup&gt;-2&lt;/sup&gt;).

||&lt;math&gt; I(\nu,T) =\frac{ 2 h\nu^{3}}{c^2}\frac{1}{ e^{\frac{h\nu}{kT}}-1} \,\!&lt;/math&gt;

&lt;math&gt;I (\lambda,T) =\frac{2 hc^2}{\lambda^5}\frac{1}{ e^{\frac{hc}{\lambda kT}}-1} &lt;/math&gt;
|-

|}

==The Assumptions of Quantum Mechanics==


{| class=&quot;wikitable&quot;
|-
| 1: State of a system
|A [[quantum state|system]] is completely specified at any one time by a [[Hilbert space]] vector.
|-
| 2: Observables of a system
|A [[observable|measurable]] quantity corresponds to an [[operational definition|operator]] with [[eigenvector]]s [[linear span|spanning]] the [[vector space|space]].
|-
| 3: Observation of a system
|Measuring a system applies the observable's operator to the system and the system [[Wave function collapse|collapses]] into the observed eigenvector.
|-
| 4: Probabilistic result of measurement
|The [[probability]] of observing an eigenvector is derived from the square of its [[wavefunction]].
|-
| 5: Time evolution of a system
|The way the wavefunction evolves over time is determined by [[Shrodinger's equation]].
|-
|}

==Quantum Numbers==


Quantum numbers are occur in the description of quantum states. There is one related to quantized atomic energy levels, and three related to quantized angular momentum.


{| class=&quot;wikitable&quot;
! Name !! Symbol !! Orbital Nomenclature !! Values 
|-

| '''Principal'''
|| ''n''
|| shell 
|| &lt;math&gt;1 \le n , n \in \mathbf{N} \,\!&lt;/math&gt; 
|-

| '''Azimuth''' 

Angular Momentum
|| ''l'' 
|| subshell;

''s'' orbital is listed as 0,

''p'' orbital as 1, 

''d'' orbital as 2, 

''f'' orbital as 3,

etc for higher orbitals
 
|| &lt;math&gt; 0 \le \ell \le n-1, \ell \in \mathbf{N} \ &lt;/math&gt; 
|-

| '''Magnetic''' 

Projection of Angular 

Momentum
|| ''m''&lt;sub&gt;''l''&lt;/sub&gt; 
|| energy shift (orientation of 

the subshell's shape)  
|| &lt;math&gt;-\ell \le m_\ell \le \ell, m_\ell \in \mathbf{N}\ &lt;/math&gt; 
|-

| '''Spin''' 

Projection of Spin 

Angular Momentum
|| ''m''&lt;sub&gt;''s''&lt;/sub&gt; 
|| spin of the electron:

-1/2 = counter-clockwise, 

+1/2 = clockwise

|| &lt;math&gt; - \begin{matrix} \frac{1}{2} \end{matrix} , \begin{matrix} \frac{1}{2} \end{matrix} \ &lt;/math&gt; 
|-
|}

==Quantum Wave-Function and Probability==

''' ''Born Interpretation of the Particle Wavefunction'' '''

Wavefunctions are probability distributions describing the space-time behaviour of a particle, distributed through space-time like a wave. It is the wave-particle duality characteristics incorperated into a mathematical function. This interpretation was due to Max Born.

''' ''Quantum Probability'' ''' 

Probability current (or flux) is a ''concept''; the ''flow of probability density''. 

The probability density is analogous to a fluid; the probability current is analogous to the fluid flow rate. In each case current is the product of density times velocity.

Usually the wave-function is dimensionless, but due to normalization integrals it may ''in general'' have dimensions of length to negative integer powers, since the integrals are with respect to space.


{| class=&quot;wikitable&quot;
|-

! Operator (Common Name/s) !! (Common) Symbol/s !! Defining Equation !! SI Unit !! Dimension
|-

| (Quantum) Wave-function
|| ''ψ'', ''Ψ'' 
|| &lt;math&gt; \psi = \psi\left ( \mathbf{r}, t \right ) \,\!&lt;/math&gt;

&lt;math&gt; \Psi = \Psi\left ( \mathbf{r}, t \right ) \,\!&lt;/math&gt;
|| m&lt;sup&gt;-n&lt;/sup&gt;
|| [L]&lt;sup&gt;-n&lt;/sup&gt;
|-


|Wavefunction, Probability Density Function
||''ρ''
||&lt;math&gt; \rho(\mathbf{r},t) = \left | \Psi (\mathbf{r},t) \right |^2 \mathrm{d}V \,\!&lt;/math&gt;
||
||
|-

|Probability Amplitude
|| ''A'', ''N''
||
||
||
|-

|Probability Current 

Flow of Probability Density
|| ''J'', ''I''
|| Non-Relativistic

&lt;math&gt;\mathbf{j} = \frac{\hbar}{2mi}\left(\Psi^* \nabla \Psi - \Psi \nabla \Psi^*\right) &lt;/math&gt;

&lt;math&gt; = \frac\hbar m \mathrm{Im}(\Psi^*\nabla\Psi) &lt;/math&gt;

&lt;math&gt;=\mathrm{Re} \left ( \Psi^* \frac{\hbar}{im} \nabla \Psi \right )&lt;/math&gt;

||
||
|-

|}

===Properties and Requirements===

''' ''Normalization Integral'' ''' 

To be solved for probability amplitude. 


''R'' = Spatial Region Particle is ''definitley'' located in (including all space)

''S'' = Boundary Surface of ''R''.


{|cellpadding=&quot;2&quot; style=&quot;border:2px solid #ccccff&quot; 
|&lt;math&gt;\int_{\mathbf{r} \in R} \left | \Psi \right |^2 \mathrm{d} V = 1 \,\!&lt;/math&gt;
|}


''' '' Law of Probability Conservation for Quantum Mechanics'' '''


{|cellpadding=&quot;2&quot; style=&quot;border:2px solid #ccccff&quot;
|&lt;math&gt;\frac{\partial}{\partial t} \int_V |\Psi|^2 \mathrm{d}V + \int_S \mathbf{j} \cdot \mathrm{d}\mathbf{A} = 0&lt;/math&gt;
|}

==Quantum Operators==


Observable quntities are calculated by operators acting on the wave-function. The term ''potential'' alone often refers to the ''potential operator'' and the ''potential term'' in Schrödinger's Equation, but this is a misconception; rather the implied quantity is ''potential '''energy''' ''. 

It is not immediatley obvious what the opeators mean in their general form, so component definitions are included in the table. Often for one-dimensional considerations of problems the component forms are useful, since they can be applied immediatley.


{| class=&quot;wikitable&quot;
|-
! Operator (Common Name/s) !! Component Definitions !! General Definition !! SI Unit !! Dimension
|-

| Position
||&lt;math&gt; \hat{x} = x \,\!&lt;/math&gt;

&lt;math&gt; \hat{y} = y \,\!&lt;/math&gt;

&lt;math&gt; \hat{z} = z \,\!&lt;/math&gt;
||&lt;math&gt; \mathbf{\hat{r}} = \mathbf{r} \,\!&lt;/math&gt;
|| m
|| [L]
|-

| Momentum
||&lt;math&gt; \hat{p}_x = -i \hbar \frac{\partial }{\partial x} \,\!&lt;/math&gt;

&lt;math&gt; \hat{p}_y = -i \hbar \frac{\partial }{\partial y} \,\!&lt;/math&gt;

&lt;math&gt; \hat{p}_z = -i \hbar \frac{\partial }{\partial z} \,\!&lt;/math&gt;
||&lt;math&gt; \mathbf{\hat{p}} = -i \hbar \nabla \,\!&lt;/math&gt;
|| J s m&lt;sup&gt;-1&lt;/sup&gt; = N s 
|| [M] [L] [T]&lt;sup&gt;-1&lt;/sup&gt;
|-

| Potential Energy
||&lt;math&gt; \hat{V}_x = V(x) \,\!&lt;/math&gt;

&lt;math&gt; \hat{V}_y = V(y) \,\!&lt;/math&gt;

&lt;math&gt; \hat{V}_z = V(z) \,\!&lt;/math&gt;
||&lt;math&gt; \hat{V} = V\left ( \mathbf{r}, t \right ) = V \,\!&lt;/math&gt;
|| J
|| [M] [L]&lt;sup&gt;2&lt;/sup&gt; [T]&lt;sup&gt;-2&lt;/sup&gt;
|-

| Energy
||
||&lt;math&gt; \hat{E} = i \hbar \frac{\partial }{\partial t} \,\!&lt;/math&gt;
|| J
|| [M] [L]&lt;sup&gt;2&lt;/sup&gt; [T]&lt;sup&gt;-2&lt;/sup&gt;
|-

| Hamiltonian
||
||&lt;math&gt; \hat{H} = \hat{T} + \hat{V} \,\!&lt;/math&gt;

&lt;math&gt;\hat{H} = -\frac{\hbar^2}{2m}\nabla^2+ V \,\!&lt;/math&gt;
|| J
|| [M] [L]&lt;sup&gt;2&lt;/sup&gt; [T]&lt;sup&gt;-2&lt;/sup&gt;
|-

| Angular Momentum
||&lt;math&gt;\hat{L}_x = -i\hbar \left(y {\partial\over \partial z} - z {\partial\over \partial y}\right)&lt;/math&gt;

&lt;math&gt;\hat{L}_y = -i\hbar \left(z {\partial\over \partial x} - x {\partial\over \partial z}\right)&lt;/math&gt;

&lt;math&gt;\hat{L}_z = -i\hbar \left(x {\partial\over \partial y} - y {\partial\over \partial x}\right)&lt;/math&gt;
||&lt;math&gt;\mathbf{\hat{L}} = -i\hbar \mathbf{r} \times \nabla &lt;/math&gt;
|| J s = N s m&lt;sup&gt;-1&lt;/sup&gt;
|| [M] [L]&lt;sup&gt;2&lt;/sup&gt; [T]&lt;sup&gt;-1&lt;/sup&gt;
|-

| Spin Angular Momentum
||&lt;math&gt; \hat{S}_x = {\hbar \over 2} \sigma_x &lt;/math&gt;

&lt;math&gt; \hat{S}_y = {\hbar \over 2} \sigma_y &lt;/math&gt;

&lt;math&gt; \hat{S}_z = {\hbar \over 2} \sigma_z &lt;/math&gt;
||
|| J s = N s m&lt;sup&gt;-1&lt;/sup&gt;
|| [M] [L]&lt;sup&gt;2&lt;/sup&gt; [T]&lt;sup&gt;-1&lt;/sup&gt;
|-

|}

==Wavefunction Equations==


''' ''Schrödinger's Equation'' '''


General form proposed by Schrödinger:


{|cellpadding=&quot;2&quot; style=&quot;border:2px solid #ccccff&quot;
|&lt;math&gt;\hat{H} \Psi = \hat{E} \Psi &lt;/math&gt;
|}


Commonly used corolaries are summarized below. A free particle corresponds to zero potential energy.

{| class=&quot;wikitable&quot;
|-
! !! 1D !! 3D 
|-

|Free Particle (V=0)
|| &lt;math&gt; - \frac{\hbar^2}{2m} \frac{\mathrm{d}^2}{\mathrm{d} x^2} \Psi = \hat{E} \Psi \,\!&lt;/math&gt;
|| &lt;math&gt; - \frac{\hbar^2}{2m} \nabla^2 \Psi = \hat{E} \Psi \,\!&lt;/math&gt;
|-

|Time Independant
|| &lt;math&gt; \left ( - \frac{\hbar^2}{2m} \frac{\mathrm{d}^2}{\mathrm{d}x^2} + V \right ) \Psi = \hat{E} \Psi \,\!&lt;/math&gt;
|| &lt;math&gt; \left ( - \frac{\hbar^2}{2m} \nabla^2 + V \right ) \Psi = \hat{E} \Psi \,\!&lt;/math&gt;
|-

|Time Dependant 
|| &lt;math&gt; \left ( - \frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + V \right ) \Psi = i \hbar \frac{\partial}{\partial t} \Psi \,\!&lt;/math&gt;
|| &lt;math&gt; \left ( - \frac{\hbar^2}{2m} \nabla^2 + V \right ) \Psi = i \hbar \frac{\partial}{\partial t} \Psi \,\!&lt;/math&gt;
|-

|}


''' ''Dirac Equation'' '''


The form proposed by Dirac is

{|cellpadding=&quot;2&quot; style=&quot;border:2px solid #ccccff&quot;
|&lt;math&gt;\left(\boldsymbol{\beta} mc^2 + c \sum_{k = 1}^3 \boldsymbol{\alpha}_k p_k \right) \Psi = i \hbar \frac{\partial}{\partial t} \Psi &lt;/math&gt;
|}


where &lt;math&gt; \boldsymbol{\beta} &lt;/math&gt; and &lt;math&gt; \boldsymbol{\alpha} &lt;/math&gt; are Dirac Matrices satisfying:


{|cellpadding=&quot;2&quot; style=&quot;border:2px solid #ccccff&quot;
|&lt;math&gt;\boldsymbol{\alpha}_i^2=\boldsymbol{\beta}^2=\mathbf{I}_4&lt;/math&gt;

&lt;math&gt;\boldsymbol{\alpha}_i\boldsymbol{\alpha}_j + \boldsymbol{\alpha}_j\boldsymbol{\alpha}_i = 0 \,&lt;/math&gt;

&lt;math&gt;\boldsymbol{\alpha}_i\boldsymbol{\beta} + \boldsymbol{\beta}\boldsymbol{\alpha}_i = 0 \,&lt;/math&gt;
|}


''' ''Klien-Gorden Equation'' '''


Schrödinger and De Broglie independantly proposed the relativistic form before Gorden and Klein, but Gorden and Klein included electromagnetic interactions into the equation, useful for charged spin-0 Bosons &lt;ref&gt;Particle Physics, B.R. Martin and G. Shaw, Manchester Physics Series 3rd Edition, 2009, {{ISBN|978-0-470-03294-7}} &lt;/ref&gt;. 


{|cellpadding=&quot;2&quot; style=&quot;border:2px solid #ccccff&quot;
|&lt;math&gt;\left(-\frac{1}{c^2}\frac{\partial^2}{\partial t^2} + \nabla^2\right)\Psi = \left ( \frac{m_0c}{\hbar} \right )^2 \Psi&lt;/math&gt;
|}


It can be obtained by inserting the quantum operators into the Momentum-Energy invariant of relativity:


&lt;math&gt; \frac{E^2}{c^2} - p^2 = \left ( m_0c \right )^2 &lt;/math&gt;


===Common Energies and Potential Energies===


The following energies are used in conjunction with Schrödinger's equation (and other variants). In fact the equation cannot be used for calculations unless the energies defined for it. 

The concept of potential energy is important in analyzing probability amplitudes, since this energy confines particles to localized regions of space; the only exception to this is the free particle subject to zero potential energy.


''V''&lt;sub&gt;0&lt;/sub&gt; = Constant Potential Energy

''E''&lt;sub&gt;0&lt;/sub&gt; = Constant Total Energy

{| class=&quot;wikitable&quot;
|-

! Potential Energy Type !! Potential Energy ''V''
|-
|Free Particle
||0
|-
|One dimensional box
|| &lt;math&gt; V = \begin{cases}
 V_0 &amp; x \in [a,b] \\
 0 &amp; x \notin [a,b]
\end{cases}
\,\!&lt;/math&gt;

|-
|Harmonic Osscilator
||&lt;math&gt; V = \frac{1}{2}kx^2 &lt;/math&gt;
|-
|Electrostatic, Coulomb
||&lt;math&gt; V = \frac{q_1 q_2}{4\pi\epsilon_0 r} &lt;/math&gt;
|-
|Electric Dipole
||&lt;math&gt; V = - \mathbf{p} \cdot \mathbf{E} &lt;/math&gt;
|-
|Magnetic Dipole
||&lt;math&gt; V = - \mathbf{m} \cdot \mathbf{B} &lt;/math&gt;
|-
|}


{| class=&quot;wikitable&quot;
|-
|-

|Infinite Potential well
|&lt;math&gt;E_n = \left ( \frac{hn}{2L} \right )^2 \frac{1}{2m}\,\!&lt;/math&gt;

&lt;math&gt; n \in \mathbf{N} \,\!&lt;/math&gt;
|-
|Wavefunction of a Trapped 

Particle, One Dimensional Box 
|&lt;math&gt;\Psi_n(x) = A \sin \left ( \frac{n\pi x}{L} \right ) \,\!&lt;/math&gt;

&lt;math&gt; n \in \mathbf{N} \,\!&lt;/math&gt;
|-
|Hydrogen atom, orbital energy
|&lt;math&gt; E_n = -\frac{me^4}{8\epsilon_0^2h^2n^2} = \frac{13.61eV}{n^2}\,\!&lt;/math&gt;

&lt;math&gt; n \in \mathbf{N} \,\!&lt;/math&gt;
|-
|}


'''Quantum Numbers'''


Expressions for various quantum numbers are given below.


{| class=&quot;wikitable&quot;
|-
|spin projection quantum number
|&lt;math&gt;m_s \in \{-1/2,+1/2\}\,\!&lt;/math&gt;
|-
|Orbital Electron Magnetic Dipole Moment
|&lt;math&gt;\mathbf{\mu}_{orb} = -e\mathbf{L}/2m\,\!&lt;/math&gt;
|-
|Orbital Electron Magnetic Dipole Components
|&lt;math&gt;\mathbf{\mu}_{orb,z} = -m_\mathcal{L}\mu_B\,\!&lt;/math&gt;
|-
|Orbital, Spin, Electron Magnetic Dipole Moment
|&lt;math&gt;\mathbf{\mu_s} = -e\mathbf{S}/m = gq\mathbf{S}/2m\,\!&lt;/math&gt;
|-
|Orbital Electron magnetic dipole moment
|&lt;math&gt;\mathbf{\mu}_{orb}=-e\mathbf{L}_{orb}/2m\,\!&lt;/math&gt;
|-
|Orbital, Spin, Electron magnetic dipole moment Potential
|&lt;math&gt;U = -\mathbf{\mu}_s\cdot\mathbf{B}_{ext} = -\mu_{s,z}B_{ext}\,\!&lt;/math&gt;
|-
|Orbital, Electron Magnetic Dipole Moment Potential
|&lt;math&gt;U = -\mathbf{\mu}_{orb}\cdot\mathbf{B}_{ext} = -\mu_{orb,z}B_{ext}\,\!&lt;/math&gt;
|-
|Angular Momentum Components
|&lt;math&gt;L_z = m\mathcal{L}\hbar\,\!&lt;/math&gt;
|-
|Spin Angular Momentum Magnitude
|&lt;math&gt;S = \hbar\sqrt{s(s+1)}\,\!&lt;/math&gt;
|-
|Cutoff Wavelength
|&lt;math&gt;\lambda_{min} = hc/K_0\,\!&lt;/math&gt;
|-
|Density of States
|&lt;math&gt;N(E) = 8\sqrt{2}\pi m^{3/2}E^{1/2}/h^3\,\!&lt;/math&gt;
|-
|Occupancy Probability
|&lt;math&gt;P(E) = 1/(e^{(E-E_F)/kT}+1)\,\!&lt;/math&gt;
|-
|}

==Spherical Harmonics==


==The Hydrogen Atom==

{| class=&quot;wikitable&quot;
|-
|Hydrogen Atom Spectrum,

Rydberg Equation
|&lt;math&gt;\frac{1}{\lambda} = R_H \left ( \frac{1}{n^2_2} - \frac{1}{n^2_1} \right )\,\!&lt;/math&gt;
|-
|Hydrogen Atom, radial probability density
|&lt;math&gt;P(r) = \frac{4r^2}{a^3e^{2r/a}}\,\!&lt;/math&gt;
|-

|}

==Multi-Electron Atoms, Perdiodic Table==
pener

== References ==

{{reflist}}

{{CourseCat}}</text>
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  </page>
  <page>
    <title>PLC/Programming basics</title>
    <ns>0</ns>
    <id>136723</id>
    <revision>
      <id>2815788</id>
      <parentid>2693138</parentid>
      <timestamp>2026-06-15T07:19:06Z</timestamp>
      <contributor>
        <username>~2026-35015-94</username>
        <id>3094230</id>
      </contributor>
      <comment>Add External links: browser-based ladder logic practice simulator</comment>
      <origin>2815788</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2189" sha1="94wyn2zizr1r8vohc2j1vix08zma5br" xml:space="preserve">Logic is integral to the programming of PLCs. 
==Logic gates==
{{Further|Wikipedia:Logic gate}}
* And gate
* Or gate
* Nor gate
* Nand gate
==Programming types==
* [[w:Ladder logic|Ladder logic]] - simplified representation of electronic schematics
==Common PLC functions==
I for input and O for output are the generally accepted standard, but some PLC manufacturers may use different letters to describe common items. 

===Inputs===
* I (Inputs) - These bits represent the connection to any external control input device wired to the PLC, including switches, buttons and motion sensors.
===Outputs===
* O (Output) - Each output bit can only be used as an output once.
===Internal bits===
Internal bits make possible almost limitless necessary logical constructs to be made.

===Latches===
[[File:BobinaNC.PNG|Ladder logic symbol&lt;/br&gt;(normally closed)|right|150px]]
Holds an electrical function on. A momentary push-button, output (from a timer or counter) or an internal bit are capable of triggering a latch. [[w:Latch (electronics)|Latches]] have the same reference as the output on the same rung. Ideally, a latch must be foolproof with an [[w:Kill switch|emergency stop]] from an input. Latches represent virtual [[w:Relay#Types|relays]].

===Timers===
* TON (Timer on) - once powered waits until its preset time to turn on the output.
* TOF (Timer off) - turns on when powered, then turns off when the preset time is reached
* RTF (Retaining timer) - are potentially dangerous as they keep count even if the PLC is reset.
===Counters===
* CTU (Counter up) - Every time this counter gets continuous power, this counter counts up. Once a function is reached it outputs.
* CTD (Counter down) - Similar to CTU, except this counts down.
===Sequencers===
Sequencers are capable of using internal [[w:Binary code|(binary)]] logic bits  to shortcut repetitive ladder logic.

==See also==
* [[Design and implementation of PLC systems]]

==External links==
* [https://plcsimulationsoftware.com/plc-simulator PLC Simulator] – browser-based ladder logic editor with scan-cycle visualisation and auto-graded practice exercises; runs with no install, free tier


[[Category:Systems engineering]]</text>
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    <title>Fluid Mechanics for Mechanical Engineers/Introduction</title>
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      <contributor>
        <username>CommonsDelinker</username>
        <id>9184</id>
      </contributor>
      <comment>Replacing Hurricane_Katrina_August_28_2005_NASA.jpg with [[File:Katrina_2005-08-28_1702Z.jpg]] (by [[:c:User:CommonsDelinker|CommonsDelinker]] because: [[:c:COM:FR|File renamed]]: Criterion 4 - conforms to other similar files' formats for storm images).</comment>
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      <text bytes="24285" sha1="ggk44862ld9h8zwtc7933vruunulzox" xml:space="preserve">==Solids, Liquids and Gases==
A fluid is composed of atoms and molecules. Depending on the [[w:Phase_(matter)|phase]] of the fluid (gas,liquid or supercritical), the distance between the molecules shows orders of magnitude difference, being the largest in the gas phase and shortest in the liquid phase. As the distance between the molecules or the [[w:Mean_free_path| mean free path]] of the flowing medium approaches to the characteristic size of the flow device, the flow cannot be treated as [[w:Continuum|continuum]].

In a solid, molecules form a regular lattice and oscillate around an equilibrium point. At this state, there is a  strong attraction between the molecules and kinetic energy of the molecules can not overcome this force in this phase of the matter.  When enough energy is given to the molecules, e.g. by heating it, the matter melts and consequently becomes a liquid. The molecules gain kinetic energy as a result of added heat and start to move around in an irregular pattern. However, the density of liquids and solids, in other words the mean molecular distances at these two phases do not differ much from each other. When the liquid vaporizes and turns into the gas phase, the density drastically drops as the molecules starts to move freely between the intermolecular collisions.


{| class=&quot;wikitable&quot;
|-
! Solid !! Liquid !! Gas
|-
| High density || High density || Low density
|-
| Low intermolecular distance (typical˜0.3 nm)  || Low intermolecular distance (typical˜0.3 nm) || High intermolecular distance (typical˜3 nm)
|-
| Low kinetic kinetic energy of molecules  || Higher kinetic energy of molecules  || Highest kinetic kinetic energy of molecules
|-
| Molecules oscillates in a regular lattice arrangement. || Molecules build lattice forms over only short distances, but they move in an irregular pattern over longer distance. || Molecules moves freely between collisions. 
|-
| Incompressible|| Hardly compressible || Compressible
|}

[[file:phases_of_matter.svg|center|600px|thumb|Cartoon showing the molecular difference between solids, liquids and gases.]]

==Definition of Fluid==

[[File:Itaipu 171.jpg|340px|right|thumb|Fluid in motion: Itaipu Dam]]

Fluid Mechanics is the study of fluids at rest (fluid statics) and in motion (fluid dynamics).

A fluid is defined as a substance that continually deforms (flows) under an applied
shear stress regardless of the magnitude of the applied stress. Whereas a solid can
resist an applied force by static deformation.
[[File:Deformation_solid_vs_fluid.png|400px|thumb|border|center|Deformation of a solid and a fluid exposed to an applied force]]


[[Wikipedia:Liquid|Liquids]], [[Wikipedia:Gas|gases]], [[Wikipedia:Plasma_(physics)|plasmas]] and, to some extent, plastic solids are accepted to be fluids. A perfect fluid offers no internal resistance to change in shape and, consequently,  they take on the shape of their containers. Liquids form a free surface (that is, a surface not created by their container) whereas gases and plasmas do not,  but, instead, they expand and occupy the entire volume of the container.
[[File:Imagen3.png|400px|thumb|border|center|Behavior of liquids, gases and plasmas in a container]]
{{clear}}

==Motivation for studying fluid mechanics==
[[File:Katrina 2005-08-28 1702Z.jpg|300px|thumb|right|Hurricane Katrina August 28 2005 NASA]]
The importance of flow phenomena is  out of question. Natural phenomena or technological applications are completely or partially involves flow phenomena. It can be met in a diverse range of length of time scales. Atmospheric flows and blood flows are two examples for this diversity. As a tool making specie, humankind learned also how to utilize flow phenomena. Hence, those, who deal with flowing matter, should be better equipped with theoretical understanding and capability to use experimental and numerical investigation tools.
[[File:Airbus A380 blue sky.jpg|400px|thumb|left|Airbus A380]]
{{clear}}

==Historical Background and Future Perspective==
[[File:Historical_Background.png|400px|thumb|right|Historical perspective to the developments in the field of fluid mechanics&lt;ref&gt;Durst, F., &quot;Grundlagen der Strömungsmechanik: Eine Einführung in die Theorie der Strömungen von Fluiden&quot;, Springer,2008.&lt;/ref&gt; ]]

Fluid mechanics have played an important role in human life. Therefore, it also attracted many curious people. Even in the ancient Greek history, systematic theoretical works have been done. The development of governing equations of fluid flow started already in the 16th century. In the 18th and 19th century, the conservation laws for mass, momentum and energy was already known in its most general form. In the 20th century, developments were in theoretical, experimental and recently numerical. In the theoretical field, mostly solutions of the governing equations for special cases were provided. Experimental methods have been developed to measure flow velocities and fluid properties. By the development of computers , the numerical treatment of fluid mechanical problems opened new perspectives in research. It is the common believe that in the 21th century, the activities would be most intensive in the  development new experimental and numerical tools and application of those for developing new technologies. 

&lt;gallery&gt;
File:Pont_du_gard.jpg|[[Wikipedia:Aquaduct|Aquaduct (Pont Du Gard), 7th cent. BC]]
File:Trireme.jpg|[[Wikipedia:Trireme|Greek ship (Trireme), 7th cent. BC]]
File:Leonardo_helicopter.JPG|[[Wikipedia:Science_and_inventions_of_Leonardo_da_Vinci|Helicopter design of Leonardo da Vinci]]
&lt;/gallery&gt;

==Basic components of Fluid Mechanics Research==
[[File:Experiments_and_simulations_train.png|250px|thumb|right|Experimental and numerical investigations conducted on a fast train.]]

Besides theoretical considerations, experiments and simulations are heavily used in research. If possible, most productive and accurate approach is the combination of all three methods. However, sometimes environmental conditions can be so harsh for any experimental technique that only theoretical or numerical methods can be used. For example, it is very hard or almost impossible to obtain the velocity or temperature distribution in the die casting mold or in the crucible used for crystal growth, because of very high temperatures.
[[File:Process_diagnostics.png|500px|thumb|center|Simulations for diagnosing crystal growth process.]]
{{clear}}

==Viscosity of a Fluid==
[[File:Deformation_of_a_fluid_element.png|500px|thumb|right|Deformation of a fluid element]]
[[File:Low viscous fluid.gif|200px|thumb|right|Deformation of a low viscous fluid under the applied stress.]]
[[File:High viscous fluid.gif|200px|thumb|right|Deformation of a high viscous fluid under the applied stress.]]

Force applied on a matter creates stresses on it. Stress is simply force per unit area:

{{center top}}&lt;math&gt; \displaystyle 
	\tau = \frac{F}{A}\left[\frac{N}{m^{2}}= Pa\right]
&lt;/math&gt;{{center bottom}}
Hence the unit of stress is &lt;math&gt; Pa &lt;/math&gt;. There can be normal and shear stresses in and on the matter.

Shear stress is proportional to the deformation rate of the matter, i.e. strain rate:
{{center top}}&lt;math&gt; \displaystyle \tau \propto \frac{\delta \theta}{\delta t}&lt;/math&gt;{{center bottom}}

{{center top}}&lt;math&gt; \displaystyle \tan{\delta\theta}= \frac{\delta u \delta t}{\delta y}&lt;/math&gt;{{center bottom}}  

&lt;math&gt; \displaystyle u&lt;/math&gt; is the deformation speed. For very small deformation angles
{{center top}}&lt;math&gt; \displaystyle 
	\delta\theta = \frac{\delta u \delta t}{\delta y} \ \rightarrow \ \frac{\delta\theta}{\delta t} = \frac{\delta u}{\delta y} \ \rightarrow \ \tau \propto \frac{\delta u}{\delta y} \ \rightarrow \ \tau = \mu \frac{\delta\theta}{\delta t} = \mu \frac{\delta u}{\delta y}
&lt;/math&gt;{{center bottom}}

&lt;math&gt; \displaystyle \mu&lt;/math&gt; is the dynamic viscosity of the fluid. 


For the same &lt;math&gt; \displaystyle \tau&lt;/math&gt; and fluid having higher viscosity &lt;math&gt; \displaystyle \mu&lt;/math&gt;, the deformation rate, i.e. velocity gradient is smaller.

Dynamic viscosity is a thermodynamic property of the material and it depends on temperature and pressure. In general, viscosity of liquids drop by increasing temperature, whereas that of gases increases. The viscosities of liquids and gases increase with increasing pressure.
{{center top}}&lt;math&gt; \displaystyle \mu=f\left(T,P\right)\left[Pa\cdot s\right]&lt;/math&gt;{{center bottom}}

Often dynamic viscosity is normalized by the density of the fluid and this quantity is called “kinematic viscosity”:
{{center top}}&lt;math&gt; \displaystyle \upsilon=\frac{\mu}{\rho}\left[\frac{m^{2}}{s}\right]&lt;/math&gt;{{center bottom}}

One can judge the dominance of inertial effects to viscous effects by using a dimensionless number, namely  Reynolds number: 
{{center top}}&lt;math&gt; \displaystyle 
	Re=\frac{\rho U_{c}l_{c}}{\mu}=\frac{U_{c} l_{c}}{\upsilon}
&lt;/math&gt;{{center bottom}}
&lt;math&gt; \displaystyle U_{c}&lt;/math&gt; and &lt;math&gt; \displaystyle l_{c}&lt;/math&gt; are characteristic velocity and length scales of the flow.
{{clear}}

==Elasticity, viscosity, solid- and liquid-like behavior, and plasticity==
[[File:Elasticity.png|200px|thumb|right|Stress and strain (deformation) relation for a solid substance]]
When one tries to deform a piece of material, some of the above properties appear depending on the amplitude and duration of the applied stress.

*'''''Long time application of weak stress'':''' '''Solids''' initially deform and then resist to deform. '''Fluids''' deform (flow) continuously.

*'''''Short time application of weak stress'':''' If deformation follows the stress, material is '''elastic!!!.''' If '''deformation rate''' follows the stress, material is '''viscous.''' 

*'''''Application of high stress'':''' After a certain stress (yield stress), some solids start to deform irreversibly. These are called '''plastic solids.'''  There are also '''yield stress fluids''', whose threshold stress is much lower than plastic solids.
{{clear}}

==Deborah number==
A transition from a more resistant (elastic) to a less resistant behavior (viscous) has a relevant characteristic time scale: '''the relaxation time of the material'''. Correspondingly, the ratio of the relaxation time of a material to the timescale of a deformation is called '''Deborah number''' :

&lt;math&gt; \displaystyle  \displaystyle De = \frac{\text{characteristic relaxation time of material}} {\text{time scale of deformation}} &lt;/math&gt;

'''Small Deborah numbers'''  correspond to situations where the material has time to relax (and behaves in a viscous manner), while '''high Deborah numbers'''  correspond to situations where the material behaves rather elastically.
Water can show elastic behavior  when the time scale of deformation becomes very short. For example, when one tries to jump to water from a height more than 100 meters, water feels like a solid ground at the instant of collision ( do not try).
'''Corn starch and water mixture'''  (suspension) is a good example with which low and high De number effects can be shown.

==Rheological Material==
Fluids can be classified according to the relation between stress &lt;math&gt; \displaystyle \tau&lt;/math&gt; and deformation rate &lt;math&gt; \displaystyle du/dy&lt;/math&gt;.
The [[Wikipedia:Newtonian_fluid|Newtonian fluids]] show a linear relation
{{center top}}&lt;math&gt; \displaystyle \tau = \mu\frac{du}{dy}\Rightarrow \mu=\mu(T,P)&lt;/math&gt;{{center bottom}}

Fluids which do not follow the linear law between stress an the deformation rate are called [[Wikipedia:Non-Newtonian_fluid|non-newtonian]] and they are the subject of [[Wikipedia:Rheology|rheology]].  A [[Wikipedia:Dilatant|dilatant (shear-thickening)]] fluid increases resistance with increasing
applied stress. Alternately, a [[Wikipedia:Pseudoplastic|pseudoplastic (shear-thinning)]] fluid decreases resistance
with increasing stress. If the thinning effect is very strong, the fluid is termed plastic. 
The limiting case of a plastic substance is one which
requires a finite yield stress before it begins to flow. The linear-flow Bingham plastic
idealization is shown in the figure, but the flow behavior after yield may also be nonlinear. Examples
of a yielding fluid are toothpaste and ketchup, which will not flow out of the tube until a finite
stress is applied by squeezing. 

Some fluids show decreasing [[Wikipedia:Thixotropy|(thixotropic)]] or  increasing resistance [[Wikipedia:Rheopecty|(rheopectic)]] in time for the same deformation rate. 
For example, pudding is a rheopectic fluid and some paints are thixotropic.

[[File:Rheological-fluids-2.png|300px|thumb|right|Types of different fluids regarding the change of the stress in time for constant a strain]]
[[File:Rheological-fluids-1.png|400px|thumb|left|Types of different fluids regarding their stress-strain dependence]]
{{clear}}
[[File:comparison_bet_solid_and_liquid_01.svg|300px|thumb|center|Comparison between solids and fluids]]

==Continuum Assumption==
[[File:Continuum_assumption_sketch.png|300px|thumb|right|Continuum assumption in a fluid flow]]
In many technical applications with gasses, the distance travelled by a molecule before it hits to another molecule ([[Wikipedia:Mean_free_path|mean free path]]) (&lt;math&gt; \displaystyle \lambda&lt;/math&gt;) are much larger than the molecular diameter.  For air, &lt;math&gt;  \lambda&lt;/math&gt; is around  &lt;math&gt; 5 \times 10^{-8}m&lt;/math&gt;.

The molecules are not fixed in a lattice but move about freely relative to each other. Thus fluid density, or mass per
unit volume, has no precise meaning because the number of molecules occupying a given volume continually changes.
If the selected unit volume &lt;math&gt; \displaystyle \delta V &lt;/math&gt; is smaller than the cube of the mean free path between the molecules, there will be large scatter in the determination of density, since the molecules move freely relative to each other, i.e. at one instant the number of molecules in the unit volume is not constant.  This effect becomes unimportant if the unit volume is large compared with, say, the cube of the molecular spacing, when the number of
molecules within the volume will remain nearly constant in spite of the enormous interchange
of particles across the boundaries. In other words, when &lt;math&gt; \displaystyle \delta V&lt;/math&gt; is selected such that the selected volume contains in average the number of molecules, the density converges to a level. The acceptable size of the  unit volume for many liquids and gases is about &lt;math&gt; \displaystyle 1\mu m^{3}&lt;/math&gt;. Over this value, the medium can be accepted as '''continuum''' , such that the variations in space and time can be accepted to be smooth and differential equations can be written to describe the fluid motion. If, however, the chosen unit volume is too large, there could be a noticeable variation within the selected volume owing to the non-uniform bulk distribution of molecules caused by temperature and/or pressure variations in the flow field.
{{clear}}

==Pressure in a fluid==
Pressure is force per unit area and is a scalar quantity.

{{center top}}&lt;math&gt; \displaystyle 
p=\frac{F}{A}\left[Pa\right]\ ; \left(1 bar = 10^{5} Pa\right)
&lt;/math&gt;{{center bottom}}


In a  fluid at rest,  the tangential viscous forces are  absent and the only force between adjacent surfaces is normal to the surface. In a resting fluid there is only a normal stress (pressure). In other words, force caused by the pressure on a surface is normal to that surface.


[[File:pressure_in_a_fluid.png|300px|thumb|right|Pressure forces on an infinitesimal fluid element]]

Balance in x-direction:

{{center top}}&lt;math&gt; \displaystyle \left(p_{1}\ ds\right)\ sin\theta - p_{3}\ dz = 0&lt;/math&gt;{{center bottom}}


{{center top}}&lt;math&gt; \displaystyle dz=ds\sin\theta\longrightarrow p_{1} = p_{3}&lt;/math&gt;{{center bottom}}


Balance in z-direction:

{{center top}}&lt;math&gt; \displaystyle -\left(p_{1}\ ds\right)\ cos\theta + p_{2}\ dx - \frac{1}{2}\rho g\ dx\ dz = 0&lt;/math&gt;{{center bottom}}


{{center top}}&lt;math&gt; \displaystyle ds\ cos\theta = dx\longrightarrow p_{2} - p_{1} - \frac{1}{2}\rho g\ dz = 0&lt;/math&gt;{{center bottom}}


For an infinitesimal prism, effect of gravity can be neglected.


{{center top}}&lt;math&gt; \displaystyle \rightarrow p_{1} = p_{2} = p_{3}&lt;/math&gt;{{center bottom}}

==Interface phenomena and surface tension==
[[File:WassermoleküleInTröpfchen.svg|thumb|250px|right|Inter molecular attraction in the liquid and on the liquid surface]]
Surface tension phenomena occur at the interface of  one liquid and another liquid, gas or a solid wall. 
The cohesive forces between molecules down into a liquid are shared with all neighboring atoms. Those on the surface have no neighboring atoms above, and exhibit stronger attractive forces upon their nearest neighbors on the surface. This enhancement of the intermolecular attractive forces at the surface is called '''surface tension.''' 

[[File:Interface_Phenomena_and_surface_tension.png|500px|thumb|center|Examples of interface and surface tension phenomena]]
{{clear}}

If the interface is curved, a mechanical balance shows that there is a pressure difference across the interface, the pressure being higher on the concave side,
{{center top}}&lt;math&gt; \displaystyle 
\Delta\ p=\sigma\left(\frac{1}{R_{1}}+\frac{1}{R_{2}}\right)
&lt;/math&gt;{{center bottom}}

where &lt;math&gt; \displaystyle \sigma\left[\frac{N}{m}\right]&lt;/math&gt; is the '''surface tension coefficient.''' Surface tension coefficient is not a property of the liquid alone, but a property of the liquid's interface with another medium.

According to the above equation, in the soap bubble or in the droplet, inner pressure is higher than outer pressure.
This can also be shown by a force balance. In the droplet, the force balance in the vertical direction reads

{{center top}}&lt;math&gt; \displaystyle F_{net}=\sigma2\pi\!R - \left(p_{i} - p_{0}\right)\pi\!R^{2}=0&lt;/math&gt;{{center bottom}}


{{center top}}&lt;math&gt; \displaystyle \Delta\ p=\sigma\frac{2}{R}&lt;/math&gt;{{center bottom}}


Similarly, in the soap bubble the force balance becomes
{{center top}}&lt;math&gt; \displaystyle \Delta\ p=\sigma\left(\frac{1}{R}+\frac{1}{R}\right)=\sigma\frac{2}{R}&lt;/math&gt;{{center bottom}}


{{center top}}&lt;math&gt; \displaystyle F_{net}=2\sigma2\pi\!R - \left(p_{i}-p_{0}\right)\pi\!R^{2}=0&lt;/math&gt;{{center bottom}}


{{center top}}&lt;math&gt; \displaystyle \Delta\ p=\sigma\frac{4}{R}&lt;/math&gt;{{center bottom}}

Note that owing to the two interfaces in the soap bubble force due to surface tension is as double as that in the droplet.

[[File:Surface_tension_Example_2.png|400px|thumb|right|Force balance in the bubble]]
[[File:Surface_tension_Example.png|400px|thumb|left|Force balance in the droplet]]
{{clear}}

The contact angle is the angle between the liquid-solid and gas-liquid interfaces. It is calculated such that angle remains in the liquid. It is dependent on the adhesion forces between the liquid molecules and the solid wall. These forces are sensitive to the actual physicochemical conditions of the solid-liquid interface. 

[[File:Wetting.svg|thumb|400px|right|Wetting]]
[[File:contact_angle.png|400px|thumb|left|Definition of contact angle]]
{{clear}}

==Saturation pressure and cavitation==
[[File:Cavitation Propeller Damage.JPG|450px|thumb|right|Cavitation Propeller Damage]]
Evaporation occurs at the liquid gas interface. When the vapor pressure of liquid is less than  the liquid's saturation pressure at the given liquid temperature, the evaporation and condensation occurs at the same time on the interface.At the liquid solid interface, at a given temperature, liquids starts to boil at saturation pressure.

[[File:Evaporation_boiling.png|350px|left|thumb|Evaporation and boiling of liquid]]
[[File:Boiling_cavitation.png|300px|left|thumb|Boiling and cavitation shown on the saturation temperature and pressure diagram of water]]

{{clear}}
Instead of increasing the temperature of the liquid, one can decrease the pressure of the liquid so that it starts to boil, or so to say '''cavitates'''.

One can meet cavitation in nature and in technical application. One known example is the cavitation damage on ship propellers. An interesting natural occurrence of cavitation was observed while the snapping shrimp hunts &lt;ref&gt;[http://stilton.tnw.utwente.nl/shrimp/ How Snapping Shrimp Snap (and flash)? ]&lt;/ref&gt;.  

==Streamline, streakline, pathline and timeline==
[[File:Aeroakustik-Windkanal-Messhalle.JPG|300px|right|thumb|Flow visualization around a car done by smoke. The lines are streaklines.]]
Four basic types of line patterns are used to visualize flows:
* A streamline is a line everywhere tangent to the velocity vector at a given instant.
* A pathline is the actual path traversed by a given fluid particle.
* A streakline is the locus of particles which have earlier passed through a prescribed point.
* A timeline is a set of fluid particles that form a line at a given instant.

In a steady flow streamlines, streaklines and pathlines are identical.
{{clear}}

==Laminar and turbulent flows==
[[File:jet_transition.png|300px|thumb|Laminar to turbulent transition of a submerged jet flow.]]
Laminar flows are:
* smooth,
* the disturbances are damped via viscous effects,
* and they are in general deterministic.

In turbulent flows:
* flow and fluid variables show random fluctuations in time and space, i.e. the flow is stochastic
* there are eddies of velocity and length scales over a very wide range

Laminar to turbulent transition occurs when the disturbances in the flow can not be damped anymore by viscous forces. This happens when the inertia of the flow is increased and/or the flow configuration (boundaries, states of the fluid(s)) causes the generation and/or amplification of very small disturbances. As Reynolds  number (Re) is the ratio of the inertial forces to viscous forces, for different types of flows, over a critical Reynolds number, transition to turbulence takes place. Below a list of simple but still technically interesting flow cases and critical Reynolds numbers are listed:

* Pipe flow: &lt;math&gt; Re=\frac{U_b D_{pipe}}{\nu} &gt; 2200 &lt;/math&gt;
* Jet flow: &lt;math&gt; Re=\frac{U_b D_{jet}}{\nu} &gt; 1000 &lt;/math&gt;
* Flow over a flat plate: &lt;math&gt; Re=\frac{U_\infty \delta_l}{\nu} &gt; 950 &lt;/math&gt;

where &lt;math&gt; U_b &lt;/math&gt;, &lt;math&gt; U_ \infty &lt;/math&gt; are the bulk velocity of the fluid  or the velocity of fluid  approaching to the plate. &lt;math&gt; D_{pipe} &lt;/math&gt;, &lt;math&gt; D_{jet} &lt;/math&gt; and &lt;math&gt; l &lt;/math&gt; are the pipe diameter, jet diameter or the length of the plate. &lt;math&gt; \delta_l= 1.72 \sqrt{ \nu l / U_\infty }&lt;/math&gt; is the displacement thickness.
{{clear}}

==Compressibility==

Ideal Gas law (Equation of State)


&lt;math&gt;\displaystyle p = \rho RT &lt;/math&gt; :  Where R is the gas constant and T is the universal temperature.


&lt;math&gt;R_{air} = 286,9 \left[\frac{J}{kg}K\right]&lt;/math&gt;

[[File:Compressibility 01.svg|250px|right|thumb|Figure: Gas under pressure]]
Density and volume change:

&lt;math&gt;\displaystyle \rho = \frac{m}{V}&lt;/math&gt;

&lt;math&gt;\displaystyle \frac{d\rho}{dV} = -\frac{m}{V^2} = -\frac{m}{V} \frac{1}{V} = -\rho \frac{1}{V}&lt;/math&gt;

&lt;math&gt;\displaystyle \frac{d\rho}{\rho} = -\frac{dV}{V}&lt;/math&gt;


The Bulk Modulus:


&lt;math&gt;\displaystyle E_{v} = - \frac{dp}{\frac{dV}{V}} = \frac{dp}{\frac{d\rho}{\rho}} \ [Pa] &lt;/math&gt;


Large values of Ev means that the fluid is relatively incompressible.


Under standard atmospheric conditions:


&lt;math&gt; E_{v} = 2.15 \times 10^{9} \ Pa = 21500\ bar\ &lt;/math&gt;  


for water and


&lt;math&gt; E_{v} = 1.42 \times 10^{5} \ Pa = 1.4\ bar\ &lt;/math&gt;  


for air. Therefore air is 15000 times more compressible than water.

Liquids can be accepted to be incompressible in many applications. Air can be compressible, especially when there are large changes of pressure in the flow.


&lt;math&gt;\frac{d\rho}{dt} = 0 &lt;/math&gt;  and  &lt;math&gt; \frac{d\rho}{dx_{i}} = 0 &lt;/math&gt; 


Where i = 1,2,3.
{{clear}}

==Classification of flows==
Following chart covers most of the flow phenomena, which might occur in a flow problem. When one deals with a flow problem, first task is to classify the flow. Correct classification helps to choose the correct and most efficient methods to deal with this problem. 
[[File:Classi.png|300px|thumb|center]]

==References==
&lt;references/&gt;

[[Category:Fluid_Mechanics_for_Mechanical_Engineers]]</text>
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      <text bytes="1824" sha1="toq63jmu7qglsdr8cw6uc6g2se8uvsl" xml:space="preserve">{{title|Tables}}

'''Tables''' can be an effective, efficient way of organising and presenting information.

==Examples==
An example of a captioned table is provided in Table 1. Each table should be referred to at least in the main body text. Another example is provided in the [[Template:Motivation_and_emotion/Book_chapter_structure#Tables|book chapter template]]. More examples can be found on this [[Motivation and emotion/Wikiversity/Tables|tables]] page. 

Table 1&lt;br&gt;''Ways to Cultivate Awe in Daily Life''
&lt;div align=&quot;center&quot;&gt;
{| class=&quot;wikitable&quot;
!Strategy
!Try it yourself
|-
|Connect with nature
|Take an [http://ggia.berkeley.edu/practice/awe_walk awe walk] (GGSC)
|-
|Consume awe-inspiring media
|Watch a [https://www.ted.com/talks Ted Talk] or listen to a [[w:Podcast|podcast]]&lt;br&gt;Watch an [http://ggia.berkeley.edu/practice/awe_video#data-tab-how awe-video] (GGSC), or choose from this [https://www.youtube.com/watch?v=9ZfN87gSjvI&amp;index=3&amp;list=PL_T9MO520krq5QsT1sIHdmBUNodksi8v2 YouTube playlist]&lt;br&gt;Watch a [https://www.youtube.com/watch?v=kbJcQYVtZMo flashmob] (YouTube, 5:40 mins)
|-
|Engage with the arts
|Read an [http://ggia.berkeley.edu/practice/awe_story awe story] (GGSC)&lt;br&gt;Visit a museum or gallery&lt;br&gt;Experience live music 
|-
|[[w:Savoring|Savour]] experiences of awe
|Look at photos, talk to other people, or [https://ggia.berkeley.edu/practice/awe_narrative# write about awe] (GGSC)
|}
&lt;/div&gt;

==Examples of chapters which make effective use of tables==
* [[Motivation and emotion/Book/2019/Organisational change motivation#Emerging themes|Organisational change motivation]] (2019)
* [[Motivation and emotion/Book/2019/Stimming motivation|Stimming motivation]] (2019)

==See also==
* [[Motivation and emotion/Wikiversity/Figures|Figures]]

[[Category:Motivation and emotion/Assessment/Chapter]]</text>
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      <text bytes="35753" sha1="05cpei2ehvdftuq9k0g15gw1ah9qqlr" xml:space="preserve">== Overview ==
[[File:Vincent E Vanity Fair 1899-04-20.jpg|thumb|alt=Old colored drawing of a man in a 19th-century black suit with grey and black striped trousers standing very erect, his hands behind his back and a full beard and moustache, looking to his left|&quot;Eastern finance&quot; (Sir Edgar Vincent) ''Vanity Fair'', 20 April 1899]]
The Duncombes, Earl (and Baron) Feversham and Viscount Helmsley really begin their branching here, with William Duncombe, 2nd Baron Feversham of Duncombe Park (on this page and [[Social Victorians/People/Duncombe#Family|the Duncombe one]]). They are related, and interrelated, by the time of the ball, but different branches.[[Social Victorians/People/Helmsley | Viscount Helmsley]] was the courtesy title for the eldest son and heir apparent of the Earl of Feversham (during the second half of the 19th century).

The people who attended the [[Social Victorians/1897 Fancy Dress Ball |Duchess of Devonshire's fancy-dress ball]] from this family are the Earl and Countess of Feversham, their 2 youngest daughters and their husbands. Probably one daughter was misidentified in the ''Lady's Pictorial'', so the 3 youngest daughters were present. Helen Vincent, Cynthia Graham and Ulrica Duncomble were sisters of William Duncombe, Viscount Helmsley, who died in 1881, so the Viscount Helmsley at the ball was his son, Charles Duncombe, the sisters' nephew. Charles's mother Muriel was also present.

== Acquaintances, Friends and Enemies ==

== Timeline ==
'''1851 August 7''', William Duncombe (at that time 2nd Baron Feversham of Duncombe Park) and Mabel Graham married.&lt;ref name=&quot;:0&quot;&gt;&quot;Mabel Violet Graham.&quot; {{Cite web|url=https://thepeerage.com/p2288.htm#i22879|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;

=== 1880s ===
'''1881 July 14, Thursday afternoon, beginning about 2 p.m.''', William, Earl of Feversham, Mabel, Countess of Feversham and Lady Hermione Duncombe were invited to a [[Social Victorians/1881-07-14 Garden Party|Garden Party at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]].

'''1881 July 22, Friday''', William, Earl of Feversham, Mabel, Countess of Feversham and Lady Hermione Duncombe were invited to — and likely attended — [[Social Victorians/1881-07-22 Marlborough House Party|the party at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]].

'''1882 July 13, Thursday''', William, Earl of Feversham, Mabel, Countess of Feversham and Lady Hermione Duncombe were invited to a [[Social Victorians/1882-07-13 Marlborough House Garden Party|Garden Party at Marlborough House for Queen Victoria]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]].

'''1884 July 03''', William, Earl of Feversham and Mabel, Countess of Feversham attended [[Social Victorians/1884-07-03 Munster Reception|Count Münster's Reception at the German Embassy]], Carlton House Terrace.

'''1886 July 21, Wednesday''', the Earl and Countess of Feversham and the Ladies Duncombe were invited to — and likely attended — [[Social Victorians/1886-07-21 Marlborough House Ball|the Ball at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]].

'''1888 March 8''', Sir Richard James Graham's father died, so he succeeded as the 4th Baronet Graham of Netherby.&lt;ref&gt;&quot;Sir Frederick Ulric Graham, 3rd Bt.&quot; {{Cite web|url=https://thepeerage.com/p5396.htm#i53954|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;

'''1889 June 27''', Lady Cynthia Duncombe and Sir Richard James Graham, 4th Baronet of Netherby married.

=== 1890s ===
'''1890 September 24''', Lady Helen Venetia Duncombe and Edgar Vincent married.&lt;ref name=&quot;:1&quot;&gt;&quot;Lady Helen Venetia Duncombe.&quot; {{Cite web|url=https://thepeerage.com/p23311.htm#i233108|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;

'''1891 July 9, Thursday''', William, Earl of Feversham seems to have been invited to a [[Social Victorians/1891-07-09 Garden Party|Garden Party at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]], to which about 3,000 people were invited.

'''1892 May 18, Wednesday''', Mabel, Countess of Feversham attended [[Social Victorians/Timeline/1892#18 May 1892, Wednesday18 May 1892, Wednesday|the Queen's Drawing-room at Buckingham Palace]] and presented Lady Ulrica Duncombe to her Royal Highness Princess Christian of Schleswig-Holstein, who held the drawing-room on behalf of Queen Victoria.

'''1894 July 19, Thursday''', William, Earl of Feversham and Lady Ulrica Duncombe attended [[Social Victorians/Timeline/1894#19 July 1894, Thursday|a ball hosted by the Duke and Duchess of Devonshire at Devonshire House that followed a dinner for the Prince and Princess of Wales]], some of their children, the Russian Ambassador, the Portuguese Minister [is this de Soveral?] and a few British dignitaries and aristocratic friends and family.

'''1897 June 28, Monday''', William, Earl of Feversham and Mabel, Countess of Feversham were invited to [[Social Victorians/Diamond Jubilee Garden Party|Queen Victoria's immense Diamond Jubilee garden party at Buckingham Palace]].

'''1897 July 2, Friday''', Lady Helen and Sir Edgar Vincent attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House as did Lord and Lady Feversham, the Earl and Countess Feversham and an as-yet-unidentified Lady Alicia Duncombe. Sir R. and Lady C. Graham were also present.

'''1897 July 31, Saturday''', William, Earl of Feversham and Mabel, Countess of Feversham gave Mabel Wombwell a &quot;silver-gilt inkstand and candlesticks&quot;&lt;ref&gt;&quot;Marriage of Mr. H. R. Hohler and Miss Wombwell.&quot; ''Morning Post'' 2 August 1897, Monday: 6 [of 8], Col. 3a–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970802/067/0006 (accessed June 2019).&lt;/ref&gt; for [[Social Victorians/Timeline/1897#31 July 1897, Saturday|her wedding to Henry R. Hohler]].

'''1899 April 20''', a caricature portrait (above right) by Leslie Ward (&quot;Spy&quot;) of &quot;Eastern Finance&quot; (Sir Edgar Vincent) appeared in this issue of ''Vanity Fair'', as Number 746 in its &quot;Men of the Day&quot; series.&lt;ref&gt;{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; (Note the differences between the figure and the shadow in this caricature.)

=== 20th Century ===
'''1926 February 20''', Edgar Vincent was created 1st Viscount D'Abernon, of Esher and Stoke D'Abernon, County Surrey.&lt;ref name=&quot;:2&quot;&gt;&quot;Edgar Vincent, 1st and last Viscount D'Abernon.&quot; {{Cite web|url=https://thepeerage.com/p23310.htm#i233094|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;

'''1936 March 2''', Edgar Vincent succeeded as the 16th Baronet Vincent, of D'Abernon, County Surrey.&lt;ref name=&quot;:2&quot; /&gt;

[[File:Helen-Venetia-ne-Duncombe-Viscountess-DAbernon-as-a-Genoese-Lady-after-Vandyck.jpg|thumb|alt=Black-and-white photograph of a standing woman richly dressed in an historical costume with a tiara and a black feather plume on top of her head|Helen Vincent as a Genoese Lady, after Vandyck. ©National Portrait Gallery, London.]]
== Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball ==

=== William, Earl of Feversham and Mabel, Countess of Feversham ===
William Ernest Duncombe, 1st Earl of Feversham and Mabel Violet Graham Duncombe, Countess Feversham were present at the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]], as were their daughters Lady Helen Vincent and Lady Cynthia Graham and their husbands. Nothing is known about the costumes of the Earl and Countess of Feversham.

=== Lady Helen Vincent ===
[[File:Den Haag - Mauritshuis - Anthony van Dyck (1599-1641) - Portrait of Anna Wake (1605-before 1669), wife of Peter Stevens 1618.jpg|thumb|left|alt=Old portrait of a woman richly dressed in black and white, with jewelry, in a gold frame|Portrait of Anna Wake, wife of Peter Stevens, by Antony Van Dyke (1618)]]
Lady Helen Vincent sat at Table 12 for the first seating for supper and was dressed as Contessa Valentina Gateago in the 17th-century procession.&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;&lt;ref name=&quot;:4&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt; Lady Helen's high status among the group of people attending the ball is revealed by her presence in the first supper seating. 

Henry Van der Weyde's portrait (above right) of &quot;Helen Venetia (née Duncombe), Viscountess D'Abernon as a Genoese Lady, after Vandyck&quot; in costume is photogravure #83 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:5&quot;&gt;&quot;Devonshire House Fancy Dress Ball (1897): photogravures by Walker &amp; Boutall after various photographers.&quot; 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.&lt;/ref&gt; The printing on the portrait says, &quot;Lady Helen Vincent as a Genoese Lady, after Vandyck.&quot;&lt;ref&gt;&quot;Helen Venetia (née Duncombe), Viscountess D'Abernon as a Genoese Lady, after Vandyck.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158441/Helen-Venetia-ne-Duncombe-Viscountess-DAbernon-as-a-Genoese-Lady-after-Vandyck.&lt;/ref&gt;

Van Dyke's 1628 portrait of Anna Wake (left) does not look like the original of Lady Helen Vincent's dress, but it shows the painter's treatment of a similar subject.

==== Commentary on Lady Vincent's Costume ====

* No newspapers described or commented on Lady Helen's dress.
* Lady Vincent's dress is a hodgepodge of elements, many Victorian but with an approximately 17th-century collar and ruffled peplum. The waist is the most notable Victorian element. The ruffles (or little puffs) at the bottom of the bodice and the pearl belt emphasize and flatter her waist, as do the broad shoulders and collar. Similar ruffles (or little puffs or ruches) also appear at the neckline.
* Lady Helen's sleeves are Victorian in how short and high they are. Although the slashed puff is a 17th-century element, its silhouette echoes the shape of sleeves popular in the 1890s. The treatment of the sleeve below the single puff is odd, difficult to know what on earth the designer was thinking, how it was constructed and what keeps it above the elbow.
* Lady Helen has pulled her skirts to the front on both sides for the photograph, distorting the front panel of the skirt slightly. The skirt appears to have stripes made by stitching strips of the same satin fabric cut from the crosswise grain, which gives this very plain skirt more texture. The center piece of the skirt is reminiscent of an underskirt. This black-and-white photograph is too dark to permit clear analysis of the features of the skirt.
* The border at the bottom of the skirt and train is stiffened — probably with horsehair — preventing the fabric from hanging straight down, resulting in an A-line. In the 1890s,&lt;blockquote&gt;Skirts were lined with cambric or taffeta and trained gowns were weighted and disciplined by facings of horsehair which might be as deep as eighteen inches at center back.&lt;ref&gt;Payne, Blanche. ''History of Costume: From the Ancient Egyptians to the Twentieth Century''. Harper &amp; Row, 1965.&lt;/ref&gt; (532)&lt;/blockquote&gt;
* This costume lacks the sophistication that would have been present in a dress designed by [[Social Victorians/People/Dressmakers and Costumiers#Mrs. Mason|Mrs. Mason]], for example, [[Social Victorians/People/Dressmakers and Costumiers#Mr. Charles Alias|Mr. Charles Alias]] or the [[Social Victorians/People/Dressmakers and Costumiers#The House of Worth|House of Worth]]. Aesthetically, the [[Social Victorians/Terminology#Frou-frou|frou-frou]] on the top is not balanced by the simplicity of the design on the skirt and train, although, because of the stripes the costume might have looked more interesting in motion than it does in this photograph.
*The photograph appears to have been retouched on the right side of Lady Helen's waist, under her right arm, a common practice.
*Lady Helen's headdress looks like a crown because of the points made by the pearls. A single black plume rises straight up from the center of the headdress.
*Lady Helen's jewelry is primarily strands of pearls with two brooch ornaments, one pendant from one of the necklaces and the other at the center of the neckline of her bodice. Besides the several strands of pearls at her neck and on her headdress are pearls on her sleeves and at her waist.
*Lady Vincent's jewels do not display the kind of wealth that someone like the Duchess of Devonshire or Mrs. Arthur Paget, for example, had.
* The wired collar should be standing up behind her head to frame her face, but the wires cannot hold up the center back because of the cut of the lace, which should have been attached differently.

[[File:Edgar-Vincent-Viscount-dAbernon-as-a-Dutch-Stadtholder-after-Frans-Hals.jpg|thumb|alt=Black-and-white photograph of a standing man richly dressed in an historical costume with a large ruff around his neck, a large hat, and a sword|Edgar Vincent as a Dutch Stadtholder, after Frans Hals. ©National Portrait Gallery, London.]]
=== Sir Edgar Vincent ===
[[File:Frans Hals 042.jpg|thumb|left|alt=Old portrait of a proud gentleman with a big white ruff, big hat, and sword|Frans Hals, ''Willem van Heythuyzen'']]
According to the newspapers, Sir Edgar Vincent was dressed as II Conte Oravio&lt;ref name=&quot;:4&quot; /&gt; or Orayio&lt;ref name=&quot;:3&quot; /&gt; in the 17th-century procession. He is not listed as having been in the first supper seating although Lady Helen Vincent is.

Henry Van der Weyde's portrait (right) of &quot;Edgar Vincent, Viscount d'Abernon as a Dutch Stadtholder after Frans Hals&quot; in costume is photogravure #84 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:5&quot; /&gt; The printing on the portrait says, &quot;Sir Edgar Vincent as a Dutch Stadtholder after Frans Hals.&quot;&lt;ref&gt;&quot;Edgar Vincent, Viscount d'Abernon as a Dutch Stadtholder after Frans Hals.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158442/Edgar-Vincent-Viscount-dAbernon-as-a-Dutch-Stadtholder-after-Frans-Hals.&lt;/ref&gt;

Van der Weyde's photograph of Sir Edgar Vincent is similar enough to Frans Hals's 1625-1630? portrait of Willem van Heythuyzen (left) that Hals's seems to be the original. Sir Edgar Vincent is striking a very similar pose, and even the photographer's drapery and set seem to refer to the Hals painting.

==== Commentary on Sir Edgar Vincent's Costume ====
The photograph of Sir Edgar is a close copy of the portrait of Willem van Heythuyzen by Frans Hals, but the clothing worn by the Victorian has been modified, as always, for the people at this ball, to accommodate standards of beauty contemporary to their own time. The painting is very dark, affecting our sense especially of the black-on-black details.

* In spite of the similarity between the two portraits, the doublet worn by Sir Edgar reflects Victorian rather than Elizabethan fashion.
* Sir Edgar's collar is not stiffened. The folds are more limp, suggesting a [[Social Victorians/Terminology#Cavalier|Cavalier]] collar, unlike the stiffened folds on the Hals portrait. But more important is that the collar in the Hals portrait has a lot of fabric, which alone can account for the fullness. Sir Edgar's collar may be starched, but it lies flatter because the costumier used so much less fabric.
* The ornament below the collar on Sir Edgar is large and probably made of lace, as is van Heythuyzen's. We cannot tell what it is or what it symbolizes.
* The fabric used for Sir Edgar's doublet and knee breeches appears to be textured, possibly a brocade or a velvet brocade. While the cloak is black like the doublet and breeches, the fabric is a more subtle, less textured brocade. Yet another fabric was used for the lining of the cloak. The textures in the fabrics are what makes this costume so sophisticated: the color is all the same.
* Sir Edgar's sleeves were made to look like they were tied to the doublet, as Elizabethan sleeves would be, but were probably sewn to it.
* The bodice of Sir Edgar's doublet is not stiffened and pointed, which changes the line of the garment, making it looser and more Victorian than Elizabethan.
* The level (rather than pointed) bodice changes the waistline and the [[Social Victorians/Terminology#Peplum|peplum]] as well.
* The garments in both portraits have decorated belts or braid at the waist. Aglets are suspended from ribbon at the waistline on both portraits.
* Sir Edgar's knee breeches and sleeves are full, so they might be padded.
* Sir Edgar's white cuffs fold back from the wrists and have tiny starched pleats and lace edging (like the cuffs in Van den Weyde's portrait), but they are not as stiffly starched. The tiny tucks or pleats in van Heythuyzen's cuffs give them stiffness and texture; Sir Edgar's cuffs are looser and less controlled.
* The buttons on the sides of the breeches look decorative rather than functional.
* The ornament at the bottom of the knee breeches actually appears to be similar in size in both portraits, but Sir Edgar's is a simple bow that is less decorative than what looks like lacy, beaded trim on van Heythuyzen.
* The shoes are dominated by the bows, which may be velvet, in the Hals portrait. Sir Edgar's bows are placed below the tongue and are smaller.
* Sir Edgar's shoes have flat heels, and the tongue rises above the bow. Van Heythuyzen's shoes appear to have wooden pattens beneath the soles.
* The metal tips attached to ribbons at the waists of the men in both portraits are [[Social Victorians/Terminology#Aglet, Aiglet|aglets or aiglets]]. Historically, breeches could be tied to the doublet with ribbons or cords whose ends were tipped with aglets. Sir Edgar's ribboned aglets are definitely decorative, but it is not clear whether Van Heythuyzen's are decorative or functional.
* Sir Edgar and Van Heythuyzen are carrying ornate cavalier rapiers. Early cavalier rapiers were long like these are, later becoming smallswords. In the portraits, the rapiers are in scabbards. Hanging from the waist of Sir Edgar's doublet is a rapier belt to hold the rapier in its scabbard. Van Heythuyzen's scabbard is quite ornate, but Sir Edgar's is simple. Both rapiers have very ornate hand guards, which is what makes them look like cavalier weapons.
* The two swords — especially the hand guards — are so like each other, did Sir Edgar find the same sword? or have this one made? Is the sword in a collection somewhere?

==== The Historical William van Heythuyzen ====
While the ''Times'' and the ''Morning Post'' say that Sir Edgar Vincent was in the 17th-century Italian procession, the description in the [[Social Victorians/1897 Fancy Dress Ball/Photographs#The Album of Photographs|commemorative album]] associates his costume with a painting rather than a person. The man in the painting is Willem van Heythuyzen, Dutch cloth merchant and , dressed in early [[Social Victorians/Terminology#Cavalier|Cavalier style]].&lt;ref name=&quot;:10&quot;&gt;{{Cite journal|date=2023-08-27|title=Willem van Heythuysen|url=https://en.wikipedia.org/w/index.php?title=Willem_van_Heythuysen&amp;oldid=1172477813|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Willem_van_Heythuysen.&lt;/ref&gt; Van Heythuyzen was the founder of Hofje van Willem Heythuijsen. (A hofje is a group of almshouses surrounding an open courtyard in which poor, elderly people, especially women, can live.&lt;ref&gt;{{Cite journal|date=2023-08-09|title=Hofje|url=https://en.wikipedia.org/w/index.php?title=Hofje&amp;oldid=1169559641|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Hofje.&lt;/ref&gt;) Hofje van Willem Heythuijsen — the hofje founded by Willem van Heythuyzen — is still in existence.&lt;ref name=&quot;:10&quot; /&gt;

=== Lady Cynthia Graham and Sir Richard Graham ===
Lady Cynthia Graham of Netherby and [[Social Victorians/People/Pless|Princess Henry of Pless]] were dressed as the Queen of Sheba and led the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; Procession]].&lt;ref name=&quot;:3&quot; /&gt;&lt;ref name=&quot;:4&quot; /&gt;{{rp|p. 7, Col. 5b}} At this time, no photograph of Lady Cynthia Graham in this costume exists. (Lady Cynthia Graham is the Earl of Feversham's youngest daugther and Sir Richard Graham's second wife.)

==== Newspaper Accounts ====
Three actual accounts of Lady Cynthia's costume exist, and two are reprinted. They are not written by fashion journalists, so what her costume looked like is difficult to imagine.
* Lady Cynthia Graham &quot;was in white satin and gauze, embroidered in gold and silver and bright rose.&quot;&lt;ref&gt;&quot;Duchess of Devonshire's Fancy Ball. A Brilliant Spectacle. Some of the Dresses.&quot; London ''Daily News'' Saturday 3 July 1897: 5 [of 10], Col. 6a–6, Col. 1b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970703/024/0005 and https://www.britishnewspaperarchive.co.uk/viewer/BL/0000051/18970703/024/0006.&lt;/ref&gt;{{rp|p. 5, Col. 7c}}
* &quot;Lady Cynthia Graham appeared as Queen of Sheba, in a robe of white Bengal satin and gauze, with embroidery of gold appliqué, satin white and cerise. The manteau was of crepon de chine, covered with embroidered gauze and appliqué of coloured satin, and studded with jewels; a ceinture and pendant were of white satin, with cerise appliqué and embroidery, and she wore a jewelled headdress.&quot;&lt;ref&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 3c}}
* &quot;Lovely Lady Cynthia Graham was one [Queen of Sheba], in white satin embroidered in gold and silver and bright rose.&quot;&lt;ref&gt;“Girls’ Gossip.” ''Truth'' 8 July 1897, Thursday: 41 [of 70], Col. 1b – 42, Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0002961/18970708/089/0041.&lt;/ref&gt;{{rp|42, Col. 1b}}
* According to the ''Carlisle Patriot'', reprinting the ''Evening Standard'' description (perhaps because Lady and Lord Graham were local), &quot;Lady Cynthia Graham of Netherby also personated the famous Eastern Queen, wearing a lovely robe of white Bengal satin and gauze, with embroidery of gold applique, satin white and cerise. The manteau was of crepon de chine, covered with embroidered gauze and applique of coloured satin, and studded with jewels; a ceinture and pendent were of white satin, with cerise applique and embroidery, and she wore a jewelled headdress.&quot;&lt;ref&gt;&quot;Fancy Dress Ball: Unparalleled Splendour.&quot; ''Carlisle Patriot'' Friday 9 July 1897: 7 [of 8], Col. 4a–b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000365/18970709/084/0007.&lt;/ref&gt;
* &quot;The other Queen of Sheba, who was Lady Cynthia Graham, was charmingly attired in white and silver and rose red.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 32, Col. 2c}}

Lady Cynthia Graham's original costume appeared in the Drury Lane production of ''The White Heather''.&lt;ref&gt;&quot;The Morning’s News.&quot; London ''Daily News'' 18 September 1897, Saturday: 5 [of 8], Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970918/027/0005.&lt;/ref&gt;

[[File:Sir Edward John Poynter - The visit of the Queen of Sheba to King Solomon - Google Art ProjectFXD.jpg|thumb|alt=Large oil painting showing a woman climbing some shallow steps to a man standing at the top in a commanding pose, both dressed in flowing robes|Sir Edward Poynter, ''The Visit of the Queen of Sheba to King Solomon'']]
==== The Queen of Sheba ====
Stories about the African Queen of Sheba appear in Jewish, Christian and Islamic traditions. She visited King Solomon with gifts and tested his wisdom. The [[Social Victorians/Victorian Things#Encyclopaedia Britannica|9th edition of the ''Encyclopaedia Britannica'']] does not have an article about the Queen of Sheba, although she figures in other, historical articles, like the one on Yemen. 

Sir Edward John Poynter's 1890 ''The Visit of the Queen of Sheba to King Solomon'' (right) is in the collection of the Art Gallery of New South Wales, which accessioned it in 1892, so it would have been available for viewing until then. The Queen of Sheba's clothing here, such as there is of it, is unlikely to have been an original for the costumes worn by Lady Cynthia Graham or Daisy, Princess Pless, but her headdress has some similarities to the one worn by [[Social Victorians/People/Goelet|May Goelet]] dressed as Scheherazade.

=== Alicia Duncombe ===
Lady Alicia Duncombe came dressed as a Greek Slave and walked in the &quot;Oriental&quot; procession.&lt;ref name=&quot;:32&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;&lt;ref name=&quot;:42&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;

Besides being mentioned twice in connection with the ball, Lady Alicia Duncombe is mentioned only once in the newspapers in the 1890s–1900s. This report from the ''Lady's Pictorial'' does not seem to be correct: Lady Helen Vincent and Lady Cynthia Graham had a sister named Ulrica, but not one named Alicia:&lt;blockquote&gt;The Earl and Countess of Feversham are at Duncombe Park, Helmsley, Yorkshire, where they will have house parties throughout the month for shooting. The Duke of Cambridge is to pay them a visit: was expected there indeed this week. Lord and Lady Feversham are the parents of that family of beautiful daughters of whom the late Duchess of Leinster was the eldest. The others are Lady Helen Vincent, Lady Cynthia Graham, and Lady Alicia Duncombe. Of their three sons one alone survives, Major the Hon. Hubert Duncombe, D.S.O. Their eldest son married and left a son, the present Viscount Helmsley. Duncombe Park has twice been burnt down. On the last occasion of a fire there Lord Feversham’s grandson, the young Duke of Leinster, was only rescued with difficulty. His Grace was on a visit to his grandparents with his two brothers, and the children were only just got away in time. The Duke of Leinster is now in his sixteenth year, but is, unfortunately, not a robust lad.&lt;ref&gt;&quot;Society Notes.&quot; ''Lady's Pictorial'' 13 September 1902, Saturday: 353 [print; 43 of 54]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005980/19020913/124/0043.&lt;/ref&gt;&lt;/blockquote&gt;Ulrica, who was a sister of Lady Helen Vincent and Lady Cynthia Graham, did not marry until 1904, and she is not mentioned anywhere as having attended the ball, so a strong possibility would be that the ''Lady's Pictorial'' got the name wrong, and Alicia Duncombe was actually Ulrica Duncombe.

== Demographics ==

=== Nationality ===
*British

=== Residences ===

* Lady Cynthia and Sir Richard Graham: Netherby Hall in the Carlisle district of Cumbria (which is why the ''Carlisle Patriot'' coverage is so thorough)&lt;ref&gt;{{Cite journal|date=2021-05-08|title=Arthuret|url=https://en.wikipedia.org/w/index.php?title=Arthuret&amp;oldid=1022099353|journal=Wikipedia|language=en}} [[wikipedia:Arthuret|https://en.wikipedia.org/wiki/Arthuret#Netherby Hall]].&lt;/ref&gt;

== Family ==
*Charles Duncombe, 1st Baron Feversham of Duncombe Park (5 December 1764 – 16 July 1841)&lt;ref name=&quot;:8&quot;&gt;&quot;Charles Duncombe, 1st Baron Feversham of Duncombe Park.&quot; {{Cite web|url=https://www.thepeerage.com/p2576.htm#i25757|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;
*Lady Charlotte Legge ( – 5 November 1848)&lt;ref&gt;&quot;Lady Charlotte Legge.&quot; {{Cite web|url=https://www.thepeerage.com/p2576.htm#i25758|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;
#Hon. Frances Duncombe (– 15 June 1881)
#Hon. Louisa Duncombe ( – 18 November 1852)
#Charles Duncombe (1795 – 1819)
#'''William Duncombe, 2nd Baron Feversham of Duncombe Park''' (14 January 1798 – 11 February 1867)
#Reverend Henry Duncombe (25 August 1800 – 1 October 1832)
#Admiral Hon. Arthur Duncombe (24 March 1806 – 6 February 1889)
#Very Rev. Augustus Duncombe (2 November 1814 – 26 January 1880)
#Hon. Octavius Duncombe (8 April 1817 – 3 December 1879)


*William Duncombe, 2nd Baron Feversham of Duncombe Park (14 January 1798 – 11 February 1867)&lt;ref name=&quot;:9&quot;&gt;&quot;William Duncombe, 2nd Baron Feversham of Duncombe Park.&quot; {{Cite web|url=https://www.thepeerage.com/p1242.htm#i12415|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;
*Lady Louisa Stewart ( – 5 March 1889)&lt;ref&gt;&quot;Lady Louisa Stewart.&quot; {{Cite web|url=https://www.thepeerage.com/p1348.htm#i13478|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;
#Hon. Gertude Duncombe ( – 24 February 1916)
#Hon. Jane Duncombe ( – 3 April 1901)
#Hon. Helen Duncombe ( – 22 November 1896)
#Hon. Albert Duncombe (11 February 1826 – 14 September 1846)
#'''William Ernest Duncombe, 1st Earl Feversham of Ryedale''' (28 January 1829 – 13 January 1915)
#Hon. Cecil Duncombe (27 May 1832 – 20 May 1902)


*William Ernest Duncombe, 1st Earl of Feversham (28 January 1829 – 13 January 1915)&lt;ref name=&quot;:6&quot;&gt;&quot;William Ernest Duncombe, 1st Earl of Feversham of Ryedale.&quot; {{Cite web|url=https://thepeerage.com/p1873.htm#i18721|title=Person Page|website=thepeerage.com|access-date=2020-11-22}}&lt;/ref&gt;
*Mabel Violet Graham Duncombe (15 February 1833 – 28 August 1915)&lt;ref name=&quot;:0&quot; /&gt;
#William Reginald Duncombe, [[Social Victorians/People/Helmsley | Viscount Helmsley]] (1 August 1852 – 24 December 1881)
#Hon. James Henry Duncombe (20 October 1853 – 10 January 1886)
#Hon. Hubert Ernest Valentine Duncombe (14 February 1862 – 21 October 1918)
#Lady Hermione Wilhelmina Duncombe (30 March 1864 – 19 March 1895)
#'''Lady Helen Venetia Duncombe''' (1866 – 16 May 1954)
#'''Lady Cynthia (Mabel Cynthia) Duncombe''' (1869 – 25 April 1926)
#'''Lady Ulrica Duncombe''' (1874? [based on presentation at Queen's drawing-room May 1892] – 27 April 1935)


*Lady Helen Venetia Duncombe ( – 16 May 1954)&lt;ref name=&quot;:1&quot; /&gt;
*Edgar Vincent, 1st and last Viscount D'Abernon (19 August 1857 – 1 November 1941)&lt;ref name=&quot;:2&quot; /&gt;


* Sir Richard James Graham, 4th Bt. (24 February 1859 – 26 August 1932)&lt;ref&gt;&quot;Sir Richard James Graham, 4th Bt..&quot; {{Cite web|url=https://thepeerage.com/p7148.htm#i71471|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;
* Olivia Baring (14 May 1863 – 21 March 1887)&lt;ref&gt;&quot;Olivia Baring.&quot; {{Cite web|url=https://thepeerage.com/p7148.htm#i71472|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;
* Lady Cynthia (Mabel Cynthia) Duncombe (1869 – 25 April 1926)&lt;ref&gt;&quot;Lady Mabel Cynthia Duncombe.&quot; {{Cite web|url=https://thepeerage.com/p1604.htm#i16038|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;
*# Lt.-Col. Sir Fergus Frederick Graham, 5th Bt. (10 March 1893 – 1 August 1978)
*# Richard Preston Graham-Vivian (10 August 1896 – 30 September 1979)
*# Daphne Graham (17 March 1903 – )


*Charles William Reginald Duncombe, 2nd Earl of Feversham (8 May 1879 – 15 September 1916)&lt;ref name=&quot;:7&quot;&gt;&quot; Charles William Reginald Duncombe, 2nd Earl of Feversham of Ryedale.&quot; {{Cite web|url=https://thepeerage.com/p2288.htm#i22880|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;
*Marjorie Blanche Eva Greville Duncombe (25 October 1884 – 25 July 1964)&lt;ref&gt;&quot;Lady Marjorie Blanche Eva Greville.&quot; {{Cite web|url=https://thepeerage.com/p2289.htm#i22881|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}&lt;/ref&gt;
#Lady Mary Diana Duncombe (19 March 1905 – October 1943)
#Charles William Slingsby Duncombe, 3rd Earl of Feversham (2 November 1906 – 4 September 1963)
#Hon. David William Ernest Duncombe (8 February 1910 – September 1927)

== Also Known As ==
*Family name: Duncombe
*Earl Feversham of Ryedale
**William Ernest Duncombe, 1st Earl of Feversham (25 July 1868 – 13 January 1915)&lt;ref name=&quot;:6&quot; /&gt;
**Charles William Reginald Duncombe, 2nd Earl of Feversham (13 January 1915 – 15 September 1916)&lt;ref name=&quot;:7&quot; /&gt;
*[[Social Victorians/People/Helmsley | Viscount Helmsley]]
**William Ernest Duncombe (25 July 1868 – 1881)&lt;ref name=&quot;:6&quot; /&gt;
**Charles William Reginald Duncombe, 2nd Earl of Feversham (24 December 1881 – 13 January 1915)&lt;ref&gt;{{Cite journal|date=2020-09-12|title=Charles Duncombe, 2nd Earl of Feversham|url=https://en.wikipedia.org/w/index.php?title=Charles_Duncombe,_2nd_Earl_of_Feversham&amp;oldid=978075739|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Baron of Feversham
**William Ernest Duncombe (11 February 1867 – )&lt;ref name=&quot;:6&quot; /&gt;
*Baron Feversham of Duncombe Park
**Charles Duncombe, 1st Baron Feversham of Duncombe Park ( – 16 July 1841)&lt;ref name=&quot;:8&quot; /&gt;
**William Duncombe, 2nd Baron Feversham of Duncombe Park (16 July 1841 – 11 February 1867)&lt;ref name=&quot;:9&quot; /&gt;
*Other [[Social Victorians/People/Duncombe | Duncombe]] families existed as well.
== Questions and Notes ==
#The newspapers call the Earl and Countess Feversham ''Lord and Lady Feversham''.
#The ''Times'' article lists Sir R. and Lady C. Graham&lt;ref name=&quot;:3&quot; /&gt;: if Lady C. Graham is Lady Cynthia, then Sir R. Graham is Sir Richard James Graham.
#Also present at the ball and accounted for on the [[Social Victorians/People/Duncombe | Duncombe page]] are the following: Alicia Duncombe, Lady and Mr. Florence Duncombe.
#Present at other social events and not accounted for were the following: Caroline Duncombe and the Misses Duncombe.
#William Duncombe, 1st Earl of Feversham is #443 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who attended]] the Duchess of Devonshire's 2 July 1897 fancy-dress ball; Mabel, Countess Feversham is #444; Lady Helen Vincent is #215; Sir Edgar Vincent is #226; Sir Edgar Vincent is #226; Lady Cynthia Graham of Netherby is #220; Sir Richard James Graham is #464.

== Footnotes ==
{{reflist}}</text>
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  <page>
    <title>Social Victorians/People/Duncombe</title>
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      <text bytes="5876" sha1="7w7fnvnqu7zu26h7ohgt91oedixkvi4" xml:space="preserve">== Overview ==
The Duncombes, Earl (and Baron) Feversham and Viscount Helmsley really begin their branching here, with [[Social Victorians/People/Feversham#Family|William Duncombe, 2nd Baron Feversham of Duncombe Park]]. They are related, and interrelated, by the time of the ball, but different branches.

== Also Known As ==
*Family name: Duncombe
*Duncombe is also the family name of the [[Social Victorians/People/Feversham | Earl of Feversham]] and [[Social Victorians/People/Helmsley|Viscount Helmsley]].

== Acquaintances, Friends and Enemies ==

== Timeline ==
'''1876 December 5''', Alfred Charles Duncombe and Lady Florence Montagu married.&lt;ref name=&quot;:1&quot;&gt;&quot;Lady Anne Florence Adelaide Montagu.&quot; {{Cite web|url=https://www.thepeerage.com/p6893.htm#i68923|title=Person Page|website=www.thepeerage.com|access-date=2020-11-25}}&lt;/ref&gt;

'''1897 July 2, Friday''', Lady Florence Duncombe and Mr. Alfred Duncombe attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House.

== Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball ==
[[File:Lady-Anne-Florence-Adelaide-Duncombe-ne-Montagu-as-a-Lady-of-the-Court-of-Marie-Stuart.jpg|thumb|alt=Black-and-white photograph of a seated woman richly dressed in an historical costume|Lady Florence Duncombe as a Lady of the Court of Marie Stuart. ©National Portrait Gallery, London.]]
Lady Florence Duncombe and Alfred Duncombe — called Mr. and Lady F. Duncombe — attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]].

Lady Florence Duncombe went, according to the ''Gentlewoman'', as an &quot;Elizabethan Court lady,&quot; wearing &quot;black silk velvet, white quilted satin studded with pearls.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 34, Col. 1c}}

Elliott &amp; Fry's portrait of &quot;Lady Anne Florence Adelaide Duncombe (née Montagu) as a Lady of the Court of Marie Stuart&quot; in costume is photogravure #258 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref&gt;&quot;Devonshire House Fancy Dress Ball (1897): photogravures by Walker &amp; Boutall after various photographers.&quot; 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.&lt;/ref&gt; The printing on the portrait says, &quot;Lady Florence Duncombe as a Lady of the Court of Marie Stuart.&quot;&lt;ref&gt;&quot;Lady Florence Duncombe as a Lady of the Court of Marie Stuart.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158621/Lady-Anne-Florence-Adelaide-Duncombe-ne-Montagu-as-a-Lady-of-the-Court-of-Marie-Stuart.&lt;/ref&gt;

This portrait was not taken at the ball or in a photographer's studio using sets and props. It looks like it was taken in someone's home.

No photograph of Alfred Duncombe is known to exist at this time.

== Demographics ==
*Nationality: British
=== Residences ===
*Calwich Abbey&lt;ref name=&quot;:0&quot;&gt;&quot;Alfred Charles Duncombe.&quot; {{Cite web|url=https://www.thepeerage.com/p6893.htm#i68922|title=Person Page|website=www.thepeerage.com|access-date=2020-11-25}}&lt;/ref&gt;
== Family ==

* Very Rev. Augustus Duncombe (2 November 1814 – 26 January 1880)&lt;ref&gt;{{Cite web|url=https://www.thepeerage.com/p2035.htm|title=Very Rev. Augustus Duncombe. Person Page 2034|website=www.thepeerage.com|access-date=2026-06-14}}&lt;/ref&gt;
* Lady Charlotte Legge ( – 5 November 1848)&lt;ref&gt;&quot;Lady Charlotte Legge.&quot; ''The Peerage: A Genealogical Survey of the Peerage of Britain as Well as the Royal Families of Europe''. Person Page 2575. https://www.thepeerage.com/p2576.htm#i25758.&lt;/ref&gt;
*# Hon. Frances Duncombe ( – 15 June 1881)
*# Hon. Louisa Duncombe ( – 18 November 1852)
*# Charles Duncombe (c. 1795–1819)
*# [[Social Victorians/People/Feversham#Family|William Duncombe, 2nd Baron Feversham of Duncombe Park]] (14 January 1798 – 11 February 1867)
*# Reverend Henry Duncombe (25 August 1800 – 1 October 1832)
*# Admiral Hon. Arthur Duncombe (24 March 1806 – 6 February 1889)
*# '''Very Rev. Augustus Duncombe''' (2 November 1814 – 26 January 1880)
*# Hon. Octavius Duncombe (8 April 1817 – 3 December 1879)


* Very Rev. Augustus Duncombe (2 November 1814 – 26 January 1880)&lt;ref&gt;{{Cite web|url=https://www.thepeerage.com/p2035.htm|title=Very Rev. Augustus Duncombe. Person Page #2034|website=www.thepeerage.com|access-date=2026-06-14}}&lt;/ref&gt;
* Lady Harriet Christian Douglas ( – 26 July 1902)&lt;ref&gt;{{Cite web|url=https://www.thepeerage.com/p2035.htm|title=Lady Harriet Christian Douglas. Person Page #2034|website=www.thepeerage.com|access-date=2026-06-14}}&lt;/ref&gt;
*# '''Alfred Charles Duncombe''' (5 June 1843 – 22 February 1925)
*# Adolphus Montagu Duncombe (6 June 1852 – 3 April 1904)


*Alfred Charles Duncombe (5 June 1843 – 22 February 1925)&lt;ref name=&quot;:0&quot; /&gt;
*Lady Florence (Anne Florence Adelaide) Montagu ( – 16 January 1940)&lt;ref name=&quot;:1&quot; /&gt;

=== Relations ===
*Lady Anne Duncombe's father was John William Montagu, [[Social Victorians/People/Sandwich|7th Earl of Sandwich]].&lt;ref name=&quot;:1&quot; /&gt;
*Her mother was [[Social Victorians/People/Paget Family|Lady Mary Paget]].&lt;ref name=&quot;:1&quot; /&gt;

== Questions and Notes ==
#Lady Florence Duncombe is #456 and Alfred Duncombe is #454 in the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of attendees]] at the ball. Lady Alicia Duncombe is #453, so in the ''Morning Post'', at least, she is mentioned when Lady Florence and Alfred Duncombe are mentioned, suggesting that they were together in the Borthwicks' minds, even though we believe her name is wrong in the ''Morning Post'' and should be Ulrica.

== Footnotes ==
{{reflist}}</text>
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    <title>Motivation and emotion/Wikiversity/Figures</title>
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      <contributor>
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        <id>10242</id>
      </contributor>
      <minor />
      <comment>/* Embedding media */</comment>
      <origin>2815688</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5635" sha1="7vsvhgs1ni44lriqqbq9c3cby6or9dq" xml:space="preserve">&lt;noinclude&gt;{{title|Working with figures}}&lt;/noinclude&gt;

[[File:Example en.svg|150px|right|thumb|'''Figure 1'''. An example image with an APA-style caption, right justified and 150px in size. &lt;nowiki&gt;[Example image]&lt;/nowiki&gt;]]

[[File:Cycling Time Trial effort.jpg|150px|right|thumb|'''Figure 2'''. A key indicator of motivation is the intensity and persistance of effort. &lt;nowiki&gt;[Example photograph]&lt;/nowiki&gt;]]

[[File:Maslow's Hierarchy of Needs.svg|360px|right|thumb|'''Figure 3'''. Maslow's hierarchy of needs represented as a pyramid, with physiological needs at the base. &lt;nowiki&gt;[Example diagram]&lt;/nowiki&gt;]]

[[File:Hypothalamus.gif|150px|right|thumb|'''Figure 4'''. The hypothalamus regulates fundamental motivations, including eating, drinking, and sex. &lt;nowiki&gt;[Example animated gif]&lt;/nowiki&gt;]]

[[File:Alzheimer's Disease.ogg|150px|right|thumb|'''Figure 5'''. This is a spoken word version of the [[w:Alzheimer's disease|Alzheimer's disease]] Wikipedia article, 2008. &lt;nowiki&gt;[Example audio]&lt;/nowiki&gt;]]

[[File:EN simpleshow foundation Fear of Flying explainer video.webm|150px|right|thumb|'''Figure 6'''. This video explains the psychology behind the fear of flying. &lt;nowiki&gt;[Example video]&lt;/nowiki&gt;]]

[[File:Basic needs.png|200px|right|thumb|'''Figure 7'''. The three basic psychological needs proposed by [[w:Self-determination theory|self-determination theory]] are considered essential ingredients for intrinsic motivation and psychological well-being.&lt;ref&gt;Figure 7 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

[[File:Implicit Motives associations.png|400px|right|thumb|'''Figure 8'''. Implicit motives affect cognition, affect, and behaviour outside conscious awareness. This diagram illustrates major sources of implicit motives.&lt;ref&gt;Figure 8 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

Figures can be a powerful way to communicate and illustrate concepts in [[Motivation and emotion/Book|motivation and emotion book chapters]] (e.g., see Figure 1). Figures can show a variety media, including:
* photographs (e.g., see Figure 2)
* diagrams (e.g., see Figure 3, Figure 7, and Figure 8)
* animated gifs (e.g., see Figure 4)
* audio (e.g., see Figure 5)
* video (e.g., see Figure 6)

The simplest way to embed media is to use material already available in [[commons:Wiki commons|Wikimedia Commons]].

Do not upload media directly to Wikiversity; upload to Wikimedia Commons instead.

==Finding media==
Only media available on Wikimedia Commons can be embedded on Wikiversity pages. Several pathways can be used to locate suitable media:
* Explore and search [[commons:Wikimedia Commons|Wikimedia Commons]] directly
* Use Wikimedia Commons search via Wikimedia tools:
** Category browsing (often structured but uneven in quality), e.g. [[commons:Category:Emotions|Category:Emotions]]
** Search results with thumbnails, e.g. [https://commons.wikimedia.org/w/index.php?search=worried worried]
** Visual Editor search (Insert → Media → File name)
* Use external search tools with licensing filters:
** [https://www.google.com/advanced_image_search Google Images Advanced Search] (set Tools → Usage rights → Creative Commons)
** [https://search.creativecommons.org/ Creative Commons search engine]
** [https://www.google.com/search?tbm=isch&amp;q=site%3Acommons.wikimedia.org Google Image search restricted to Commons]
* See the [[Motivation and emotion/Gallery|motivation and emotion gallery]] for some starting images

==Uploading to Wikimedia Commons==
Media may be uploaded to Commons if:
* Equivalent media isn't already available on Commons
* You created the media or it is licensed for free reuse (e.g., Creative Commons Attribution or public domain)
* The media is educational

Upload process:
* Go to [[c:|Wikimedia Commons]]
* Select Upload Wizard
* Provide required metadata, including:
** Copyright owner
** Licence type
** Description of image

Once uploaded to Commons, media can be embedded in Wikiversity pages (e.g., see Figures 7 to 8)

==Embedding media==
Media can be inserted on a Wikiversity page using the Visual Editor:
* Edit page → Insert → Media → File
* Add:
** Caption
** Size
**Position

Best practice:
* Ensure media content directly supports surrounding text
* Use consistent numbering across figures within a page
* Add at least one in-text citation (e.g., see Figure 1)

==Customise figure presentation==
Figures should follow clear academic conventions:
* Size
** Optimise for viewing (not too large or small)
** Increase size for complex diagrams requiring readability
* Position
** Right alignment is standard for text flow
** Centre alignment is suitable for conceptual models or key figures
** Left alignment is rarely used
* Captions
** Must be descriptive and interpretable without the main text
* Referencing
** Each figure must be explicitly cited in text (e.g., see Figure 1)
* Integration
** Figures must directly support the argument or explanation in adjacent text

==See also==
* [[Template:Motivation and emotion/Book chapter structure#Figures|Figures]] (Motivation and emotion book chapter template)
* [[Help:Wikitext quick reference#Images, tables, video, and sounds|Images, tables, video, and sounds]] (Wikiversity help page)
* [[Help:Media|Media]] (Wikiversity help page)
* [[Motivation and emotion/Assessment/Chapter/Tables|Tables]] (Motivation and emotion book chapter help page)

==References==
{{reflist}}
&lt;noinclude&gt;
[[Category:Motivation and emotion/Wikiversity]]
[[Category:Motivation and emotion/Assessment/Chapter]]&lt;/noinclude&gt;</text>
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        <id>10242</id>
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      <text bytes="5635" sha1="ltkent4l2jkk5dbowp9gqmlwk7h6jn6" xml:space="preserve">&lt;noinclude&gt;{{title|Working with figures}}&lt;/noinclude&gt;

[[File:Example en.svg|150px|right|thumb|'''Figure 1'''. An example image with an APA-style caption, right justified and 150px in size. &lt;nowiki&gt;[Example image]&lt;/nowiki&gt;]]

[[File:Cycling Time Trial effort.jpg|150px|right|thumb|'''Figure 2'''. A key indicator of motivation is the intensity and persistance of effort. &lt;nowiki&gt;[Example photograph]&lt;/nowiki&gt;]]

[[File:Maslow's Hierarchy of Needs.svg|360px|right|thumb|'''Figure 3'''. Maslow's hierarchy of needs represented as a pyramid, with physiological needs at the base. &lt;nowiki&gt;[Example diagram]&lt;/nowiki&gt;]]

[[File:Hypothalamus.gif|200px|right|thumb|'''Figure 4'''. The hypothalamus regulates fundamental motivations, including eating, drinking, and sex. &lt;nowiki&gt;[Example animated gif]&lt;/nowiki&gt;]]

[[File:Alzheimer's Disease.ogg|200px|right|thumb|'''Figure 5'''. This is a spoken word version of the [[w:Alzheimer's disease|Alzheimer's disease]] Wikipedia article, 2008. &lt;nowiki&gt;[Example audio]&lt;/nowiki&gt;]]

[[File:EN simpleshow foundation Fear of Flying explainer video.webm|200px|right|thumb|'''Figure 6'''. This video explains the psychology behind the fear of flying. &lt;nowiki&gt;[Example video]&lt;/nowiki&gt;]]

[[File:Basic needs.png|200px|right|thumb|'''Figure 7'''. The three basic psychological needs proposed by [[w:Self-determination theory|self-determination theory]] are considered essential ingredients for intrinsic motivation and psychological well-being.&lt;ref&gt;Figure 7 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

[[File:Implicit Motives associations.png|400px|right|thumb|'''Figure 8'''. Implicit motives affect cognition, affect, and behaviour outside conscious awareness. This diagram illustrates major sources of implicit motives.&lt;ref&gt;Figure 8 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

Figures can be a powerful way to communicate and illustrate concepts in [[Motivation and emotion/Book|motivation and emotion book chapters]] (e.g., see Figure 1). Figures can show a variety media, including:
* photographs (e.g., see Figure 2)
* diagrams (e.g., see Figure 3, Figure 7, and Figure 8)
* animated gifs (e.g., see Figure 4)
* audio (e.g., see Figure 5)
* video (e.g., see Figure 6)

The simplest way to embed media is to use material already available in [[commons:Wiki commons|Wikimedia Commons]].

Do not upload media directly to Wikiversity; upload to Wikimedia Commons instead.

==Finding media==
Only media available on Wikimedia Commons can be embedded on Wikiversity pages. Several pathways can be used to locate suitable media:
* Explore and search [[commons:Wikimedia Commons|Wikimedia Commons]] directly
* Use Wikimedia Commons search via Wikimedia tools:
** Category browsing (often structured but uneven in quality), e.g. [[commons:Category:Emotions|Category:Emotions]]
** Search results with thumbnails, e.g. [https://commons.wikimedia.org/w/index.php?search=worried worried]
** Visual Editor search (Insert → Media → File name)
* Use external search tools with licensing filters:
** [https://www.google.com/advanced_image_search Google Images Advanced Search] (set Tools → Usage rights → Creative Commons)
** [https://search.creativecommons.org/ Creative Commons search engine]
** [https://www.google.com/search?tbm=isch&amp;q=site%3Acommons.wikimedia.org Google Image search restricted to Commons]
* See the [[Motivation and emotion/Gallery|motivation and emotion gallery]] for some starting images

==Uploading to Wikimedia Commons==
Media may be uploaded to Commons if:
* Equivalent media isn't already available on Commons
* You created the media or it is licensed for free reuse (e.g., Creative Commons Attribution or public domain)
* The media is educational

Upload process:
* Go to [[c:|Wikimedia Commons]]
* Select Upload Wizard
* Provide required metadata, including:
** Copyright owner
** Licence type
** Description of image

Once uploaded to Commons, media can be embedded in Wikiversity pages (e.g., see Figures 7 to 8)

==Embedding media==
Media can be inserted on a Wikiversity page using the Visual Editor:
* Edit page → Insert → Media → File
* Add:
** Caption
** Size
**Position

Best practice:
* Ensure media content directly supports surrounding text
* Use consistent numbering across figures within a page
* Add at least one in-text citation (e.g., see Figure 1)

==Customise figure presentation==
Figures should follow clear academic conventions:
* Size
** Optimise for viewing (not too large or small)
** Increase size for complex diagrams requiring readability
* Position
** Right alignment is standard for text flow
** Centre alignment is suitable for conceptual models or key figures
** Left alignment is rarely used
* Captions
** Must be descriptive and interpretable without the main text
* Referencing
** Each figure must be explicitly cited in text (e.g., see Figure 1)
* Integration
** Figures must directly support the argument or explanation in adjacent text

==See also==
* [[Template:Motivation and emotion/Book chapter structure#Figures|Figures]] (Motivation and emotion book chapter template)
* [[Help:Wikitext quick reference#Images, tables, video, and sounds|Images, tables, video, and sounds]] (Wikiversity help page)
* [[Help:Media|Media]] (Wikiversity help page)
* [[Motivation and emotion/Assessment/Chapter/Tables|Tables]] (Motivation and emotion book chapter help page)

==References==
{{reflist}}
&lt;noinclude&gt;
[[Category:Motivation and emotion/Wikiversity]]
[[Category:Motivation and emotion/Assessment/Chapter]]&lt;/noinclude&gt;</text>
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      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>+ Creating media</comment>
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      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5895" sha1="pw38czpop3gm5jlz38779bg329jt107" xml:space="preserve">&lt;noinclude&gt;{{title|Working with figures}}&lt;/noinclude&gt;

[[File:Example en.svg|150px|right|thumb|'''Figure 1'''. An example image with an APA-style caption, right justified and 150px in size. &lt;nowiki&gt;[Example image]&lt;/nowiki&gt;]]

[[File:Cycling Time Trial effort.jpg|150px|right|thumb|'''Figure 2'''. A key indicator of motivation is the intensity and persistance of effort. &lt;nowiki&gt;[Example photograph]&lt;/nowiki&gt;]]

[[File:Maslow's Hierarchy of Needs.svg|360px|right|thumb|'''Figure 3'''. Maslow's hierarchy of needs represented as a pyramid, with physiological needs at the base. &lt;nowiki&gt;[Example diagram]&lt;/nowiki&gt;]]

[[File:Hypothalamus.gif|200px|right|thumb|'''Figure 4'''. The hypothalamus regulates fundamental motivations, including eating, drinking, and sex. &lt;nowiki&gt;[Example animated gif]&lt;/nowiki&gt;]]

[[File:Alzheimer's Disease.ogg|200px|right|thumb|'''Figure 5'''. This is a spoken word version of the [[w:Alzheimer's disease|Alzheimer's disease]] Wikipedia article, 2008. &lt;nowiki&gt;[Example audio]&lt;/nowiki&gt;]]

[[File:EN simpleshow foundation Fear of Flying explainer video.webm|200px|right|thumb|'''Figure 6'''. This video explains the psychology behind the fear of flying. &lt;nowiki&gt;[Example video]&lt;/nowiki&gt;]]

[[File:Basic needs.png|200px|right|thumb|'''Figure 7'''. The three basic psychological needs proposed by [[w:Self-determination theory|self-determination theory]] are considered essential ingredients for intrinsic motivation and psychological well-being.&lt;ref&gt;Figure 7 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

[[File:Implicit Motives associations.png|400px|right|thumb|'''Figure 8'''. Implicit motives affect cognition, affect, and behaviour outside conscious awareness. This diagram illustrates major sources of implicit motives.&lt;ref&gt;Figure 8 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

Figures can be a powerful way to communicate and illustrate concepts in [[Motivation and emotion/Book|motivation and emotion book chapters]] (e.g., see Figure 1). Figures can show a variety media, including:
* photographs (e.g., see Figure 2)
* diagrams (e.g., see Figure 3, Figure 7, and Figure 8)
* animated gifs (e.g., see Figure 4)
* audio (e.g., see Figure 5)
* video (e.g., see Figure 6)

The simplest way to embed media is to use material already available in [[commons:Wiki commons|Wikimedia Commons]].

Do not upload media directly to Wikiversity; upload to Wikimedia Commons instead.

==Finding media==
Only media available on Wikimedia Commons can be embedded on Wikiversity pages. Several pathways can be used to locate suitable media:
* Explore and search [[commons:Wikimedia Commons|Wikimedia Commons]] directly
* Use Wikimedia Commons search via Wikimedia tools:
** Category browsing (often structured but uneven in quality), e.g. [[commons:Category:Emotions|Category:Emotions]]
** Search results with thumbnails, e.g. [https://commons.wikimedia.org/w/index.php?search=worried worried]
** Visual Editor search (Insert → Media → File name)
* Use external search tools with licensing filters:
** [https://www.google.com/advanced_image_search Google Images Advanced Search] (set Tools → Usage rights → Creative Commons)
** [https://search.creativecommons.org/ Creative Commons search engine]
** [https://www.google.com/search?tbm=isch&amp;q=site%3Acommons.wikimedia.org Google Image search restricted to Commons]
* See the [[Motivation and emotion/Gallery|motivation and emotion gallery]] for some starting images

==Creating media==
You can create your own media by:
* Taking a photograph
* Drawing a diagram
* [[Commons:Graphic Lab/Illustration workshop|Requesting an illustration]]
* [[c:Commons:AI-generated media|Using artificial intelligence]] may also be appropriate

==Uploading to Wikimedia Commons==
Media may be uploaded to Commons if:
* Equivalent media isn't already available on Commons
* You created the media or it is licensed for free reuse (e.g., Creative Commons Attribution or public domain)
* The media is educational

Upload process:
* Go to [[c:|Wikimedia Commons]]
* Select Upload Wizard
* Provide required metadata, including:
** Copyright owner
** Licence type
** Description of image

Once uploaded to Commons, media can be embedded in Wikiversity pages (e.g., see Figures 7 to 8)

==Embedding media==
Media can be inserted on a Wikiversity page using the Visual Editor:
* Edit page → Insert → Media → File
* Add:
** Caption
** Size
**Position

Best practice:
* Ensure media content directly supports surrounding text
* Use consistent numbering across figures within a page
* Add at least one in-text citation (e.g., see Figure 1)

==Customise figure presentation==
Figures should follow clear academic conventions:
* Size
** Optimise for viewing (not too large or small)
** Increase size for complex diagrams requiring readability
* Position
** Right alignment is standard for text flow
** Centre alignment is suitable for conceptual models or key figures
** Left alignment is rarely used
* Captions
** Must be descriptive and interpretable without the main text
* Referencing
** Each figure must be explicitly cited in text (e.g., see Figure 1)
* Integration
** Figures must directly support the argument or explanation in adjacent text

==See also==
* [[Template:Motivation and emotion/Book chapter structure#Figures|Figures]] (Motivation and emotion book chapter template)
* [[Help:Wikitext quick reference#Images, tables, video, and sounds|Images, tables, video, and sounds]] (Wikiversity help page)
* [[Help:Media|Media]] (Wikiversity help page)
* [[Motivation and emotion/Assessment/Chapter/Tables|Tables]] (Motivation and emotion book chapter help page)

==References==
{{reflist}}
&lt;noinclude&gt;
[[Category:Motivation and emotion/Wikiversity]]
[[Category:Motivation and emotion/Assessment/Chapter]]&lt;/noinclude&gt;</text>
      <sha1>pw38czpop3gm5jlz38779bg329jt107</sha1>
    </revision>
    <revision>
      <id>2815699</id>
      <parentid>2815697</parentid>
      <timestamp>2026-06-14T22:34:45Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Expand Creating media with assistance of ChatGPT: https://chatgpt.com/share/6a2f2c6b-3f58-83ec-93e3-fdaff56f34b2</comment>
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      <text bytes="7268" sha1="cive54xltrgcm1o1741qesghqlls4eu" xml:space="preserve">&lt;noinclude&gt;{{title|Working with figures}}&lt;/noinclude&gt;

[[File:Example en.svg|150px|right|thumb|'''Figure 1'''. An example image with an APA-style caption, right justified and 150px in size. &lt;nowiki&gt;[Example image]&lt;/nowiki&gt;]]

[[File:Cycling Time Trial effort.jpg|150px|right|thumb|'''Figure 2'''. A key indicator of motivation is the intensity and persistance of effort. &lt;nowiki&gt;[Example photograph]&lt;/nowiki&gt;]]

[[File:Maslow's Hierarchy of Needs.svg|360px|right|thumb|'''Figure 3'''. Maslow's hierarchy of needs represented as a pyramid, with physiological needs at the base. &lt;nowiki&gt;[Example diagram]&lt;/nowiki&gt;]]

[[File:Hypothalamus.gif|200px|right|thumb|'''Figure 4'''. The hypothalamus regulates fundamental motivations, including eating, drinking, and sex. &lt;nowiki&gt;[Example animated gif]&lt;/nowiki&gt;]]

[[File:Alzheimer's Disease.ogg|200px|right|thumb|'''Figure 5'''. This is a spoken word version of the [[w:Alzheimer's disease|Alzheimer's disease]] Wikipedia article, 2008. &lt;nowiki&gt;[Example audio]&lt;/nowiki&gt;]]

[[File:EN simpleshow foundation Fear of Flying explainer video.webm|200px|right|thumb|'''Figure 6'''. This video explains the psychology behind the fear of flying. &lt;nowiki&gt;[Example video]&lt;/nowiki&gt;]]

[[File:Basic needs.png|200px|right|thumb|'''Figure 7'''. The three basic psychological needs proposed by [[w:Self-determination theory|self-determination theory]] are considered essential ingredients for intrinsic motivation and psychological well-being.&lt;ref&gt;Figure 7 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

[[File:Implicit Motives associations.png|400px|right|thumb|'''Figure 8'''. Implicit motives affect cognition, affect, and behaviour outside conscious awareness. This diagram illustrates major sources of implicit motives.&lt;ref&gt;Figure 8 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

Figures can be a powerful way to communicate and illustrate concepts in [[Motivation and emotion/Book|motivation and emotion book chapters]] (e.g., see Figure 1). Figures can show a variety media, including:
* photographs (e.g., see Figure 2)
* diagrams (e.g., see Figure 3, Figure 7, and Figure 8)
* animated gifs (e.g., see Figure 4)
* audio (e.g., see Figure 5)
* video (e.g., see Figure 6)

The simplest way to embed media is to use material already available in [[commons:Wiki commons|Wikimedia Commons]].

Do not upload media directly to Wikiversity; upload to Wikimedia Commons instead.

==Finding media==
Only media available on Wikimedia Commons can be embedded on Wikiversity pages. Several pathways can be used to locate suitable media:
* Explore and search [[commons:Wikimedia Commons|Wikimedia Commons]] directly
* Use Wikimedia Commons search via Wikimedia tools:
** Category browsing (often structured but uneven in quality), e.g. [[commons:Category:Emotions|Category:Emotions]]
** Search results with thumbnails, e.g. [https://commons.wikimedia.org/w/index.php?search=worried worried]
** Visual Editor search (Insert → Media → File name)
* Use external search tools with licensing filters:
** [https://www.google.com/advanced_image_search Google Images Advanced Search] (set Tools → Usage rights → Creative Commons)
** [https://search.creativecommons.org/ Creative Commons search engine]
** [https://www.google.com/search?tbm=isch&amp;q=site%3Acommons.wikimedia.org Google Image search restricted to Commons]
* See the [[Motivation and emotion/Gallery|motivation and emotion gallery]] for some starting images

==Creating media==
Creating your own media is often the best way to illustrate psychological concepts because it allows you to tailor the content to the topic. Original media uploaded to Wikimedia Commons allows others to use, which is a [[Motivation and emotion/Assessment/Social contribution|social contribution]].

You can create your own media by:
* Taking photographs
* Drawing diagrams, models, flowcharts, timelines, or concept maps
* Creating graphs, charts, or infographics based on research findings
* Recording audio (e.g., pronunciations, interviews, or narrated explanations)
* Creating videos, animations, or screencasts
* Using [[Commons Lab/Illustration workshop|Commons Graphic Lab]] to request assistance with illustrations, diagrams, maps, or image improvements
* Using [[c:Commons media|artificial intelligence tools]] where appropriate and in accordance with Wikimedia Commons policies

Student-created diagrams are particularly valuable because they can:
* Simplify complex psychological theories and research
* Visually represent relationships between concepts
* Improve reader understanding and engagement
* Demonstrate your own interpretation and synthesis of the literature

When creating media:
* Aim for accuracy, clarity, and simplicity
* Use readable text and labels
* Ensure that colours, symbols, and formatting enhance understanding
* Create media that can be understood independently of the surrounding text
* Consider accessibility (e.g., colour contrast, descriptive captions, and alternative text)

Before creating new media, check whether suitable material already exists on Wikimedia Commons.

==Uploading to Wikimedia Commons==
Media may be uploaded to Commons if:
* Equivalent media isn't already available on Commons
* You created the media or it is licensed for free reuse (e.g., Creative Commons Attribution or public domain)
* The media is educational

Upload process:
* Go to [[c:|Wikimedia Commons]]
* Select Upload Wizard
* Provide required metadata, including:
** Copyright owner
** Licence type
** Description of image

Once uploaded to Commons, media can be embedded in Wikiversity pages (e.g., see Figures 7 to 8)

==Embedding media==
Media can be inserted on a Wikiversity page using the Visual Editor:
* Edit page → Insert → Media → File
* Add:
** Caption
** Size
**Position

Best practice:
* Ensure media content directly supports surrounding text
* Use consistent numbering across figures within a page
* Add at least one in-text citation (e.g., see Figure 1)

==Customise figure presentation==
Figures should follow clear academic conventions:
* Size
** Optimise for viewing (not too large or small)
** Increase size for complex diagrams requiring readability
* Position
** Right alignment is standard for text flow
** Centre alignment is suitable for conceptual models or key figures
** Left alignment is rarely used
* Captions
** Must be descriptive and interpretable without the main text
* Referencing
** Each figure must be explicitly cited in text (e.g., see Figure 1)
* Integration
** Figures must directly support the argument or explanation in adjacent text

==See also==
* [[Template:Motivation and emotion/Book chapter structure#Figures|Figures]] (Motivation and emotion book chapter template)
* [[Help:Wikitext quick reference#Images, tables, video, and sounds|Images, tables, video, and sounds]] (Wikiversity help page)
* [[Help:Media|Media]] (Wikiversity help page)
* [[Motivation and emotion/Assessment/Chapter/Tables|Tables]] (Motivation and emotion book chapter help page)

==References==
{{reflist}}
&lt;noinclude&gt;
[[Category:Motivation and emotion/Wikiversity]]
[[Category:Motivation and emotion/Assessment/Chapter]]&lt;/noinclude&gt;</text>
      <sha1>cive54xltrgcm1o1741qesghqlls4eu</sha1>
    </revision>
    <revision>
      <id>2815700</id>
      <parentid>2815699</parentid>
      <timestamp>2026-06-14T22:37:14Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <minor />
      <comment>/* Creating media */</comment>
      <origin>2815700</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="7243" sha1="kk1txgl5w3m4mdv7dv739wh7jtmhhe4" xml:space="preserve">&lt;noinclude&gt;{{title|Working with figures}}&lt;/noinclude&gt;

[[File:Example en.svg|150px|right|thumb|'''Figure 1'''. An example image with an APA-style caption, right justified and 150px in size. &lt;nowiki&gt;[Example image]&lt;/nowiki&gt;]]

[[File:Cycling Time Trial effort.jpg|150px|right|thumb|'''Figure 2'''. A key indicator of motivation is the intensity and persistance of effort. &lt;nowiki&gt;[Example photograph]&lt;/nowiki&gt;]]

[[File:Maslow's Hierarchy of Needs.svg|360px|right|thumb|'''Figure 3'''. Maslow's hierarchy of needs represented as a pyramid, with physiological needs at the base. &lt;nowiki&gt;[Example diagram]&lt;/nowiki&gt;]]

[[File:Hypothalamus.gif|200px|right|thumb|'''Figure 4'''. The hypothalamus regulates fundamental motivations, including eating, drinking, and sex. &lt;nowiki&gt;[Example animated gif]&lt;/nowiki&gt;]]

[[File:Alzheimer's Disease.ogg|200px|right|thumb|'''Figure 5'''. This is a spoken word version of the [[w:Alzheimer's disease|Alzheimer's disease]] Wikipedia article, 2008. &lt;nowiki&gt;[Example audio]&lt;/nowiki&gt;]]

[[File:EN simpleshow foundation Fear of Flying explainer video.webm|200px|right|thumb|'''Figure 6'''. This video explains the psychology behind the fear of flying. &lt;nowiki&gt;[Example video]&lt;/nowiki&gt;]]

[[File:Basic needs.png|200px|right|thumb|'''Figure 7'''. The three basic psychological needs proposed by [[w:Self-determination theory|self-determination theory]] are considered essential ingredients for intrinsic motivation and psychological well-being.&lt;ref&gt;Figure 7 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

[[File:Implicit Motives associations.png|400px|right|thumb|'''Figure 8'''. Implicit motives affect cognition, affect, and behaviour outside conscious awareness. This diagram illustrates major sources of implicit motives.&lt;ref&gt;Figure 8 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

Figures can be a powerful way to communicate and illustrate concepts in [[Motivation and emotion/Book|motivation and emotion book chapters]] (e.g., see Figure 1). Figures can show a variety media, including:
* photographs (e.g., see Figure 2)
* diagrams (e.g., see Figure 3, Figure 7, and Figure 8)
* animated gifs (e.g., see Figure 4)
* audio (e.g., see Figure 5)
* video (e.g., see Figure 6)

The simplest way to embed media is to use material already available in [[commons:Wiki commons|Wikimedia Commons]].

Do not upload media directly to Wikiversity; upload to Wikimedia Commons instead.

==Finding media==
Only media available on Wikimedia Commons can be embedded on Wikiversity pages. Several pathways can be used to locate suitable media:
* Explore and search [[commons:Wikimedia Commons|Wikimedia Commons]] directly
* Use Wikimedia Commons search via Wikimedia tools:
** Category browsing (often structured but uneven in quality), e.g. [[commons:Category:Emotions|Category:Emotions]]
** Search results with thumbnails, e.g. [https://commons.wikimedia.org/w/index.php?search=worried worried]
** Visual Editor search (Insert → Media → File name)
* Use external search tools with licensing filters:
** [https://www.google.com/advanced_image_search Google Images Advanced Search] (set Tools → Usage rights → Creative Commons)
** [https://search.creativecommons.org/ Creative Commons search engine]
** [https://www.google.com/search?tbm=isch&amp;q=site%3Acommons.wikimedia.org Google Image search restricted to Commons]
* See the [[Motivation and emotion/Gallery|motivation and emotion gallery]] for some starting images

==Creating media==
Creating media is sometimes the best way to illustrate psychological concepts because it allows you to tailor the content to the topic. Original media uploaded to Wikimedia Commons allows others to use, which is a [[Motivation and emotion/Assessment/Social contribution|social contribution]].

You can create your own media by:
* Taking photographs
* Drawing diagrams, models, flowcharts, timelines, or concept maps
* Creating graphs, charts, or infographics based on research findings
* Recording audio (e.g., pronunciations, interviews, or narrated explanations)
* Creating videos, animations, or screencasts
* Using the [[Commons Lab/Illustration workshop|Commons Graphic Lab]] to request assistance with improving or creating images
* Using [[c:Commons media|artificial intelligence tools]] where appropriate and in accordance with Wikimedia Commons policies

Student-created diagrams are particularly valuable because they can:
* Simplify complex psychological theories and research
* Visually represent relationships between concepts
* Improve reader understanding and engagement
* Demonstrate your own interpretation and synthesis of the literature

When creating media:
* Aim for accuracy, clarity, and simplicity
* Use readable text and labels
* Ensure that colours, symbols, and formatting enhance understanding
* Create media that can be understood independently of the surrounding text
* Consider accessibility (e.g., colour contrast, descriptive captions, and alternative text)

Before creating new media, check whether suitable material already exists on Wikimedia Commons.

==Uploading to Wikimedia Commons==
Media may be uploaded to Commons if:
* Equivalent media isn't already available on Commons
* You created the media or it is licensed for free reuse (e.g., Creative Commons Attribution or public domain)
* The media is educational

Upload process:
* Go to [[c:|Wikimedia Commons]]
* Select Upload Wizard
* Provide required metadata, including:
** Copyright owner
** Licence type
** Description of image

Once uploaded to Commons, media can be embedded in Wikiversity pages (e.g., see Figures 7 to 8)

==Embedding media==
Media can be inserted on a Wikiversity page using the Visual Editor:
* Edit page → Insert → Media → File
* Add:
** Caption
** Size
**Position

Best practice:
* Ensure media content directly supports surrounding text
* Use consistent numbering across figures within a page
* Add at least one in-text citation (e.g., see Figure 1)

==Customise figure presentation==
Figures should follow clear academic conventions:
* Size
** Optimise for viewing (not too large or small)
** Increase size for complex diagrams requiring readability
* Position
** Right alignment is standard for text flow
** Centre alignment is suitable for conceptual models or key figures
** Left alignment is rarely used
* Captions
** Must be descriptive and interpretable without the main text
* Referencing
** Each figure must be explicitly cited in text (e.g., see Figure 1)
* Integration
** Figures must directly support the argument or explanation in adjacent text

==See also==
* [[Template:Motivation and emotion/Book chapter structure#Figures|Figures]] (Motivation and emotion book chapter template)
* [[Help:Wikitext quick reference#Images, tables, video, and sounds|Images, tables, video, and sounds]] (Wikiversity help page)
* [[Help:Media|Media]] (Wikiversity help page)
* [[Motivation and emotion/Assessment/Chapter/Tables|Tables]] (Motivation and emotion book chapter help page)

==References==
{{reflist}}
&lt;noinclude&gt;
[[Category:Motivation and emotion/Wikiversity]]
[[Category:Motivation and emotion/Assessment/Chapter]]&lt;/noinclude&gt;</text>
      <sha1>kk1txgl5w3m4mdv7dv739wh7jtmhhe4</sha1>
    </revision>
    <revision>
      <id>2815702</id>
      <parentid>2815700</parentid>
      <timestamp>2026-06-14T22:38:54Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <minor />
      <origin>2815702</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="7249" sha1="omxt0qahzlbtljvr7hwo787barmsqe3" xml:space="preserve">&lt;noinclude&gt;{{title|Working with figures}}&lt;/noinclude&gt;

[[File:Example en.svg|150px|right|thumb|'''Figure 1'''. An example image with an APA-style caption, right justified and 150px in size. &lt;nowiki&gt;[Example image]&lt;/nowiki&gt;]]

[[File:Cycling Time Trial effort.jpg|150px|right|thumb|'''Figure 2'''. A key indicator of motivation is the intensity and persistance of effort. &lt;nowiki&gt;[Example photograph]&lt;/nowiki&gt;]]

[[File:Maslow's Hierarchy of Needs.svg|360px|right|thumb|'''Figure 3'''. Maslow's hierarchy of needs represented as a pyramid, with physiological needs at the base. &lt;nowiki&gt;[Example diagram]&lt;/nowiki&gt;]]

[[File:Hypothalamus.gif|200px|right|thumb|'''Figure 4'''. The hypothalamus regulates fundamental motivations, including eating, drinking, and sex. &lt;nowiki&gt;[Example animated gif]&lt;/nowiki&gt;]]

[[File:Alzheimer's Disease.ogg|200px|right|thumb|'''Figure 5'''. This is a spoken word version of the [[w:Alzheimer's disease|Alzheimer's disease]] Wikipedia article, 2008. &lt;nowiki&gt;[Example audio]&lt;/nowiki&gt;]]

[[File:EN simpleshow foundation Fear of Flying explainer video.webm|200px|right|thumb|'''Figure 6'''. This video explains the psychology behind the fear of flying. &lt;nowiki&gt;[Example video]&lt;/nowiki&gt;]]

[[File:Basic needs.png|200px|right|thumb|'''Figure 7'''. The three basic psychological needs proposed by [[w:Self-determination theory|self-determination theory]] are considered essential ingredients for intrinsic motivation and psychological well-being.&lt;ref&gt;Figure 7 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

[[File:Implicit Motives associations.png|400px|right|thumb|'''Figure 8'''. Implicit motives affect cognition, affect, and behaviour outside conscious awareness. This diagram illustrates major sources of implicit motives.&lt;ref&gt;Figure 8 was created by a Motivation and emotion student in 2020 and uploaded to [[c:|Wikimedia Commons]].&lt;/ref&gt;]]

'''Figures''' can be a powerful way to communicate and illustrate concepts in [[Motivation and emotion/Book|motivation and emotion book chapters]] (e.g., see Figure 1). Figures can show a variety media, including:
* photographs (e.g., see Figure 2)
* diagrams (e.g., see Figure 3, Figure 7, and Figure 8)
* animated gifs (e.g., see Figure 4)
* audio (e.g., see Figure 5)
* video (e.g., see Figure 6)

The simplest way to embed media is to use material already available in [[commons:Wiki commons|Wikimedia Commons]].

Do not upload media directly to Wikiversity; upload to Wikimedia Commons instead.

==Finding media==
Only media available on Wikimedia Commons can be embedded on Wikiversity pages. Several pathways can be used to locate suitable media:
* Explore and search [[commons:Wikimedia Commons|Wikimedia Commons]] directly
* Use Wikimedia Commons search via Wikimedia tools:
** Category browsing (often structured but uneven in quality), e.g. [[commons:Category:Emotions|Category:Emotions]]
** Search results with thumbnails, e.g. [https://commons.wikimedia.org/w/index.php?search=worried worried]
** Visual Editor search (Insert → Media → File name)
* Use external search tools with licensing filters:
** [https://www.google.com/advanced_image_search Google Images Advanced Search] (set Tools → Usage rights → Creative Commons)
** [https://search.creativecommons.org/ Creative Commons search engine]
** [https://www.google.com/search?tbm=isch&amp;q=site%3Acommons.wikimedia.org Google Image search restricted to Commons]
* See the [[Motivation and emotion/Gallery|motivation and emotion gallery]] for some starting images

==Creating media==
Creating media is sometimes the best way to illustrate psychological concepts because it allows you to tailor the content to the topic. Original media uploaded to Wikimedia Commons allows others to use, which is a [[Motivation and emotion/Assessment/Social contribution|social contribution]].

You can create your own media by:
* Taking photographs
* Drawing diagrams, models, flowcharts, timelines, or concept maps
* Creating graphs, charts, or infographics based on research findings
* Recording audio (e.g., pronunciations, interviews, or narrated explanations)
* Creating videos, animations, or screencasts
* Using the [[Commons Lab/Illustration workshop|Commons Graphic Lab]] to request assistance with improving or creating images
* Using [[c:Commons media|artificial intelligence tools]] where appropriate and in accordance with Wikimedia Commons policies

Student-created diagrams are particularly valuable because they can:
* Simplify complex psychological theories and research
* Visually represent relationships between concepts
* Improve reader understanding and engagement
* Demonstrate your own interpretation and synthesis of the literature

When creating media:
* Aim for accuracy, clarity, and simplicity
* Use readable text and labels
* Ensure that colours, symbols, and formatting enhance understanding
* Create media that can be understood independently of the surrounding text
* Consider accessibility (e.g., colour contrast, descriptive captions, and alternative text)

Before creating new media, check whether suitable material already exists on Wikimedia Commons.

==Uploading to Wikimedia Commons==
Media may be uploaded to Commons if:
* Equivalent media isn't already available on Commons
* You created the media or it is licensed for free reuse (e.g., Creative Commons Attribution or public domain)
* The media is educational

Upload process:
* Go to [[c:|Wikimedia Commons]]
* Select Upload Wizard
* Provide required metadata, including:
** Copyright owner
** Licence type
** Description of image

Once uploaded to Commons, media can be embedded in Wikiversity pages (e.g., see Figures 7 to 8)

==Embedding media==
Media can be inserted on a Wikiversity page using the Visual Editor:
* Edit page → Insert → Media → File
* Add:
** Caption
** Size
**Position

Best practice:
* Ensure media content directly supports surrounding text
* Use consistent numbering across figures within a page
* Add at least one in-text citation (e.g., see Figure 1)

==Customise figure presentation==
Figures should follow clear academic conventions:
* Size
** Optimise for viewing (not too large or small)
** Increase size for complex diagrams requiring readability
* Position
** Right alignment is standard for text flow
** Centre alignment is suitable for conceptual models or key figures
** Left alignment is rarely used
* Captions
** Must be descriptive and interpretable without the main text
* Referencing
** Each figure must be explicitly cited in text (e.g., see Figure 1)
* Integration
** Figures must directly support the argument or explanation in adjacent text

==See also==
* [[Template:Motivation and emotion/Book chapter structure#Figures|Figures]] (Motivation and emotion book chapter template)
* [[Help:Wikitext quick reference#Images, tables, video, and sounds|Images, tables, video, and sounds]] (Wikiversity help page)
* [[Help:Media|Media]] (Wikiversity help page)
* [[Motivation and emotion/Assessment/Chapter/Tables|Tables]] (Motivation and emotion book chapter help page)

==References==
{{reflist}}
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      <text bytes="38494" sha1="oy3njq18ks0yvvpymwavag44zpddjbd" xml:space="preserve">{{title|Natural disasters and emotion:&lt;br&gt;How do people respond emotionally to natural disasters and how can they be supported?}}
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==Overview==
{{Display box|content=
[[File:2003 Canberra Firestorm-Woden.jpg|thumb|The sky during the 2003 Canberra bushfires disaster.]]
When I was eight I experienced my first ever natural disaster, the 2003 Canberra Bushfires. When the fire arrived I had an all encompassing feeling of terror, I didn’t fully understand what exactly was going on but I knew I was in danger. My dad however was focused and determined to get our family to safety. We didn’t know where my mother was as we were arriving back from a holiday when the fire hit. My mum chose to stay at home to look after my younger brother who was only a baby. When we arrived to the street I lived on, the entire suburb was ablaze. My dad told me and my sister to stay in the car while he went to see if my mum was still inside our home. Shielding his eyes he dashed past the flames coming from the house at the end of the street, a moment of bravery that he says to this day was his most fearful moment.

Thankfully he survived, he couldn’t find my mum or brother, so he took us to our grandparents house assuming my mum would have gone there to make sure they were okay. He wasn’t wrong, my grandmother said she did come here but they sent her to the evacuation centre which was set up at a local college. They didn’t go with her because the fire was heading towards their house and they wanted to grab a few things. My dad refused their insistence he go as well to the evacuation centre and instead stayed to help them.

We made it to the evacuation centre, and there were crowds of people, all talking to one another. The evacuation centre personnel didn’t seem to know what to do with everyone, but looking back on it, we kind of just all automatically worked together to get comfortable that night. People were already helping one another to find family members, and a lovely lady helped us find my mum. Although she was covered in ash, she was alive and well. I haven’t had many tears of joy in my life but that moment was one of them, when we all hugged as a family.

Fast forward to 2019, once again disaster had struck. The southern Canberra suburbs were in the line of the Orrorall Valley fire. People were being readied to evacuate should the need arise, yet at no point did I feel afraid for my safety, but I was very afraid for my dad's safety. He was no longer the young man able to run into the flames for others.  I spent that entire week at his place ensuring I was ready to help if needed.|title=My Family, Fire and Fear|url=}}

The above story about my families{{gr}} experiences with bushfires possibly seems a bit strange. There is the usual emotions one would expect from a disaster—fear. Yet that fear isn’t just about ones{{gr}} own survival, there’s more to the fear both me and my family experienced. Theres{{gr}} also feelings of joy in the story, {{gr}} how could a traumatic experience like a disaster illicit the emotion of joy? As we explore the psychology of emotions relating to natural disasters, hopefully you will see there is {{gr}} explanations for these emotions.

Additionally it is crucial to understand that although emotions during disasters are experienced individually, they are rarely experienced alone. Natural disasters impact individually but also impact whole communities of people. The harsh reality is that more people and communities will experience natural disasters, as they are only increasing due to climate change (World Meteorological Association, 2021). Now is the best time to understand the emotions in relation to disasters. This chapter draws heavily from studies of survivors of natural disasters to describe the emotions at play, as well as providing evidence based methods for supporting peoples emotions when disaster strikes.

Before we even explore the emotions, it is a good idea to gain an understand the stages of a disaster in an emotional context. According to Myers &amp; Wee  (2005), emotions and when they occur during a disaster can be best understood when dividing a disasters lifespan into different sections. Those sections being the pre-disaster, Impact, honeymoon, disillusionment and restructuring{{gr}}. Keep these phases in mind as you read about the emotions and how to support yourself and others with their emotions

== Phases of disaster recovery ==
[[File:Phases of Disaster recpvery.jpg|thumb|Phases of Disaster recovery as adapted from Myer &amp; Wee (2005)|left]]

{{fact}}

'''Pre-disaster Phase:''' This is the phase when knowledge of a disaster is present and individuals act accordingly to prevent harm, {{gr}}this phase is often logic driven based on advice or prior experience

'''Impact phase:''' This is the phase when the disaster hits and individuals are most likely to experience purely survival minded emotions  

'''Honeymoon phase:''' this is the phase where relief is experienced and safety is commonly found following the impact of the disaster, {{gr}} following this stage with the right conditions some individuals can go on to restructure their understanding of the experience in a healthy manner. If they don’t have the right conditions they become disillusioned

'''Disillusionment phase:''' This is when individuals feel distressing emotions and franticly search for ways to cope, {{gr}} this phase often results in negative outcomes unless individuals are provided the right tools to cope positively. This phase can lead people to re-experience the impact of the disaster, even when they are safe 

'''Restructuring phase:''' This is when individuals begin the path of acceptance, and rebuild their life and communities. '' ''

==How do people react emotionally to natural disasters?==
It is a common assumption that emotions relating to natural disaster are mostly fear-based, and pass when the disaster subsides. While it is true that fear is one of the most common emotional reactions to a disaster, it is by no means the only one. Further, fear can have a multitude of different presentations in the context of a disaster. Emotions are not a singular event when it comes to traumatic life experiences, {{gr}} multiple emotions can occur simultaneously, and at different times during the course of a disaster. 

==== Fear ====
Given fear is one of the most commonly associated emotions connected with mass threats like natural disasters (Espinola, et al. 2016), it perhaps is the best emotion to start exploring. Fear is one of the core emotions, {{gr}} it is often considered to be negative; however fear serves its purpose by encouraging us to find safety from a threat (Steimer, 2002). One of the most commonly used definitions of fear is that it is an emotion in response to a known adverse environmental stimuli, both before the stimulus is present and/or within its presence (Steimer, 2002). What is important to remember with fear is that it is a known threat, when we experience fear we are aware of what the threat is or might be.

A good place to start with fear is to look at it from inside the brain. There is a structure in the brain called the amygdala, {{gr}} its responsible for recognising threats and relaying messages to other areas of the brain (Öhman, 2005). This is done to begin the process of causing a bodily reaction that culminates in the fight, flight or freeze response. The amygdala upon recognising a threat sends a signal to the hypothalamus, which then relays this signal to the pituitary gland to release adrenocorticotropic hormone (ACTH) into the blood stream (Grey &amp; Bingaman, 1996). ACTH’s main function is to increase epinephrine production from the adrenal gland. Epinephrine plays an important role in enabling the bodily requirements for the immediate fight, flight or freeze response (Kozlowska, et al. 2015). 

[[File:Amygdala.jpg|center|thumb|Location of the Amygdala]]

During the fight, flight or freeze response the parasympathetic nervous system prioritises bodily functions typically needed for survival (McCory, 2007). Muscles become tense, heart rate and breathing increases and digestion slows; this aids us in automatically doing what or body decides needs to be done in order to ensure our survival in the face of something that has caused the fear. During a disaster scenario it is not uncommon to hear of people talking about being so afraid they ran faster than they thought they ever could, pulling off feats of strength they didn’t know they could do or completely being frozen by fear. This all comes down to the brain and how it processes fear in the face of an imminent threat to our survival.{{fact}}

It is understandable given how our body reacts to fear to think it is only about ones{{gr}} own safety when presented with a threat. This may not be entirely accurate when it comes to disasters. In 2016-2017, central Italy was impacted by earthquakes, {{gr}} hundreds of people lost their lives and many structures were destroyed (Mollaioli, et al. 2019). A study by Massazza, Brewin &amp; Joffee (2021) looking into the ‘peritraumatic reactions’ or the thoughts, feelings and behaviours due to trauma found survivors of Italys{{gr}} earthquakes had an interesting experience with fear. The studies participants were asked in an interview setting to describe how they felt during the impact of the disaster; 78 percent of the 104 participants mentioned feeling fear for the safety of others and 70 percent mentioned feeling fear for their own safety. This shows that fear during a disaster may not just be an emotional response about ones{{gr}} own wellbeing but also the wellbeing of others.

{{Display box|title=Thought Time: Lingering fear|content=With the Italian earthquake study they also found that majority of the participants were struck with continual increased general fear and anxiety. When we experience a major threat to ourselves and others the fear and anxiety we experience can sometimes become ongoing even when the threat passes. The amygdala is responsible for recognising something fearful and readying our response, yet it serves another purpose. A study by Duvarci, Bauer &amp; Pare (2009) found that aside from sending signals to hormone response areas of the brain the amygdala also sends messages to an area known as the bed nucleus of the stria terminalis. They found that the bed nucleus is critical for long term generalised emotional arousal, {{gr}} the more significant a message is sent between the amygdala and the bed nucleus the more likely one will experience ongoing general fear that something may occur. 

Think of a time you have experienced intense fear, {{gr}} did that feeling linger? If it did, how long did it last? And was that fear the same intensity as what you originally experienced?}}

Young adults across cultures have been observed to experience less fear of being harmed by natural disasters than older adults or young children. A study of Macedonian, Turkish and Serbian young adults found a markedly increased fear for others than themselves pre-disaster, {{gr}} specifically there was fear across all three countries for their parents and childrens{{gr}} safety (Cvetkovic, Ocal &amp; Ivanov, 2019). This could be an example of ‘sandwich generational squeeze’ which is the name for the phenomenon that is young to middle age adults feeling compelled to attend the needs of both their elderly parents as well as their own children (Brody, 2003). In a disaster scenario, as the need is one relating to survival, it’s possible the fear for the survival of the elderly and children outweighs the feelings of fear for ones{{gr}} own survival. 

==== Sadness ====
Sadness is also common during times of disaster, {{gr}} often sadness presents in the honeymoon and disillusionment phases of a disasters. Once the threat has abated, even with the knowledge it wasn’t their fault, individuals can experience intense sadness (Izard, 1991). One of the reasons this could be is due to an individual having time to assess their loss in the aftermath of the disaster. What can happen following this assessment and experiencing the accompanying sadness, an individual may attempt to regain some control as a means to cope with their loss (Vandervoort, 2001). This was seen at play with hurricane Katrina; the higher the loss the individual experienced after the storm the more they would drink or smoke in an effort to not experience intense feelings of sadness (Flory, et al. 2009). There was even increased instances of addiction amongst the impacted communities following Katrina (Beaudoin, 2011).

[[File:Katrina 2005-08-28 1702Z.jpg|left|thumb|Hurricane Katrina as seen from space]]

It is not just vices such as alcohol people use to avoid experiencing sadness and loss of control. Researchers looking at consumption and buying habits post-Katrina found a significant number of the population were buying needless items directly after the disaster (Sneath, Lacey &amp; Kennett-Hensel, 2009). Participants of the consumption study struggled to explain why they purchased so many items but a common reason put forward was often that they didn’t like seeing all their possessions destroyed and feeling incredibly sad even distressed because of this. One of the participants{{gr}} impulse bought because they felt numb due to sadness and wanted to feel more positive. Impulse buying has an emotional component (Eysenck et al,.1985), and its driven in a disaster scenario by a need to restore how we felt prior to the disaster, or reduce the emotional impact in the moment of experiencing loss.

==== Anger ====
Anger arises when there is something in the way of a goal we care about, {{gr}} sometimes this can be a small event, or it can be massive like a disaster destroying your community (Stephens &amp; Groeger, 2011). Anger is most often seen much later following a disaster, usually in the disillusionment and restructuring phases. The anger is commonly directed towards failings on a community level. Anger makes individuals far more likely to recognise injustices (Keltner, Ellsworth &amp; Edwards, 1993); when local authorities fail to provide the needs of a community during a disaster, no matter how inevitable, it is often responded to with aggression. Anger is also a precursor to change and adaptation, {{gr}} it sends the message that this injustice will not be accepted again. As an emotion, anger is less about motivating ourselves and more about ensuring others are motivated to do better.  

While we think of anger as a negative emotion, in the aftermath of a disaster it actually serves a positive purpose. Anger in the wake of a disaster can lead to collective action by a community, {{gr}} this action can even involve individuals who are not impacted by the disaster (Vestergren, Uysal &amp; Tekin 2022). This collective action occurs mostly due to anger from the disaster shedding light on the disproportionate effects on minority or vulnerable groups (Templeton, et al. 2020). Members of the community may then band together in anger and frustration at the injustice,{{gr}} this creates a sense of shared identity and increased community connection (Cocking, et al., 2009). This spurs change, and is vital in building a more connected and disaster resilient community in the future.

{{Display box|title=Thought Time: Common Fate|content=There exists an idea amongst disaster literature about ‘common fate’, {{gr}} common fate explains why we don’t take an every man for themselves approach to a disaster, {{gr}} instead we often turn towards one another even with little knowledge of who the other person is. Drury, et al. (2010) interviewed groups of individuals who experienced various disasters and nearly all of the groups spoke of the sense of connection and shared support during each of the disasters. The researchers suggest the reason for this comes down to how we recognise a common fate, and that all other ideas of who an individual is dissipates, we then view each other on the same social level. As we have seen; fear, sadness and anger are never just about ourselves during times of disaster. Some element of our emotions during times of disaster are involving others.

Do you think ‘common fate’ may provide a possible reason why during times of natural disaster there’s almost always emotion involving others?}}

==== Joy ====
Joy is just as common as negative emotions during a disaster, during the honeymoon phase of the disaster it is one of the positive emotions people experience most{{fact}}. In El Salvadore, during the days following a devastating earthquake, survivors in the evacuation centre reported experiencing joy (Vazquez, et al. 2005). The adult survivors spoke specifically about the joy of being alive, and of their family members surviving. They also spoke about being given the chance to connect to the community and that increased the shared sense of joy amongst the adults. The children within the centre spoke specifically of the joy relating to the positive experiences at the evacuation centre, as well as being given time to spend with their peers.{{fact}} 

Social media is also an effective way to examine emotions in real time during the course of a disaster. Social media posts during the Kerala floods in India showed that overall there was an increase in positive sentiment, such as joy, within tweets after the immediate impact of the disaster, as opposed to negative sentiment during the impact (Mendon, et al. 2021). Joy can actually enable us to broaden our perspectives (Fredrickson, 1998); so the joy at spending time with family may have broadened individuals views on the impact of the disaster from a negative to a positive experience. The social media posts and evacuation experiences could also indicate people engaging in reappraisals, or reshaping the experience to a more positive emotion (John &amp; Gross, 2004). This would aid another effect joy has, which is its ability to sooth our overall experience (Levenson, 1999), even when that experience is a traumatic one.

==== Quiz ====
&lt;quiz display=simple&gt;
{Question one: Which of these is a TRUE statement about fear and disasters
|type=&quot;()&quot;}
+ It's common to experience fear for others, not just ourselves during a disaster.
- We only fear for our own survival.
- The hypothalamus is the main area of the brain responsible for fear.
- Fear causes a bodily response that only requires the amygdala.

{Fill in the blank
|type=&quot;{}&quot;}
Following the assessment of damage and experiencing sadness an individual may attempt to limit their perceived lack of { control } through impulsive { buying }. 

{Which of these is a TRUE statement about sadness and disaster
|type=&quot;()&quot;}
+ Sadness is often the result of assessing damage and loss.
- The sadness is short lives and goes away quickly.
- There's no connection between addiction and sadness.
- Impulse buying has no relation to sadness.

{Fill in the blank 
|type=&quot;{}&quot;} 
Anger following a disaster isn't always negative, it can in fact spur { collective } { action }. This is due to the disaster shedding light on injustice within the community.
&lt;/quiz&gt;

== How can those affected be supported? ==
Now that we know the different types of emotions, its{{gr}} time to look at how we can support peoples{{gr}} emotional well being over the course of a disaster. There’s no sure-fire right or wrong way to support yourself or others to cope. Some ways may work better than others, but it all comes down to the individual. To understand ways of supporting yourself and others we will break down the different potential methods by the different phases of the disaster.

{{fact}}

==== Pre-disaster ====
Effective and clear communication is key in this phase, {{gr}}this is not just about communicating the best methods for preparation but also about communicating information on what the disaster even is. It's a good idea to encourage people you know, and even yourself to read local emergency services communications on the disaster. The more individuals understand exactly what they will be facing the more likely they are to experience reduced fear and still act in a manner which best supports their survival (Bonanno &amp; Gupta, 2012). For vulnerable groups communication needs to be adapted to best support their situation, in some cases using plain direct language will be important or providing information directly instead of via computer devices (Howard, Bevis &amp; Blackmore, 2017),

Reach out to your elderly family members, and vulnerable people you know. If you are worried about their safety, work with them on setting up an evacuation or emergency plan before a disaster strikes. This is particularly important for supporting those you know with a disability, or increased needs when the disaster impacts. This will help to calm any fears you may have for their safety and enable you the ability to prioritise your own emergency plan. 

{{Display box|title=Thought Time: Disaster ready|content=With your disaster plan, its a good idea to consider the following: 
{{ic|Use bullet points}}

-What you plan on taking from your residence?

-Do you have your id documents in one spot?

-Do you have any items that cant be replace that you could easily transport?

-What medications, medical equipment or other health related items you will require?

-Who are your emergency contacts?

-What to do about your pets, where will they stay, how will you transport them?

BUT, you should also consider these things:

-What is something that helps keep you calm when you are stressed?

-Do you know already how you react in high intensity situations? have you written this down so family members or emergency personnel can easily understand how you are behaving?

Your disaster plan should also incorporate your mental wellbeing, it cant just be about your physical safety!}}

==== Impact phase ====
Supporting emotions during the impact phase can only commence once an individual has found safety. Governments ensuring adequate facilities for shelter is crucial, this also means adequate facilities for vulnerable communities such as the elderly and those with disabilities. Supporting vulnerable groups has been identified as a key improvement area cross-culturally in impact disaster response (Kako, et al. 2020). If not already implemented emergency personnel should be made aware at a local level of any vulnerable members of the community who may require additional support. Disability services should engage with their clients on how the evacuation, and shelter process is going to work and what supports will be available. 

Once adequate safety is obtained, individuals have time to asses their situation, this is when negative emotions like sadness and fear for others are most likely to start arising. Use the time while sheltering to speak with someone you trust, vocalising how you are feeling can help to alleviate some of the fear. Reduce over usage of news material, aim to only access news material that relates to your specific situation (like emergency broadcasts), over indulging in news can increase fear (Bodas, et al. 2015). This also applies to social media, aim to only use it to reach out to converse with family and friends instead of scrolling for more information on the unfolding disaster.

==== Honey-moon phase ====
This phase is the best time to build and encourage positive habits in the wake of the disaster. Firstly alcohol and other vices should be avoided as a means of coping, as we saw above this can lead to addiction. If you are going to engage in addictive substances it is best to do it in a positive social situation and place a limit on yourself. 

Another method for supporting your emotional wellbeing is to engage in a regular routine, this creates a sense of normalcy even in the absence of normal. This could be as simple as setting a specific time to get up each morning, or creating a meal plan to follow. Something that is consistent and regular will help to reduce lingering feelings of fear by increasing a sense of ‘normal’ (Bonnano, et al, 2007)

Lastly during this phase, avoid making big life decisions, {{gr}} when we have gone through a period of emotional turmoil we don’t have the best judgment (Ross III &amp; Coambs, 2018 ). If a big life decision does present itself, allow or request time to consider it, don’t be afraid of explaining the reason you need time. As you saw above its common for others to understand and accept that you will be struggling for abit  given the situation. Its best to not add any additional stress during the honeymoon phase.

==== Disillusionment phase ====
If you feel your emotions becoming overwhelming or increasingly negative post-disaster you are likely in the disillusionment phase. For supporting emotions during this phase it's all about social connection. As with the impact phase, voicing how you feel to someone you trust can alleviate the immediate pressure or distress you may feel. For young adults and teenagers this is particularly important, as increased negative emotions during this phase can turn towards criminality (Nuttman-Shwartz, 2019). With teenagers if their emotions are leaning towards negative coping strategies, It may be a good idea to include them in simple community rebuilding tasks as an effective way of creating purpose, social connection and providing a sense of accomplishment. Teenagers are highly adaptable in turning negative emotions relating to disasters into positive community action (Nuttman-Shwartz, 2019)


For adults support groups are a good way to meet others in similar situations and to engage in emotional reciprocation. When we share how we feel with others who understand the situation we often gain new perspectives and feel a reduction in negative emotions, this is known as situation modification (Lazarus &amp; Folkman, 1984). This is also a perfect time to practice reappraisals, which as we saw above in the section on joy, is when we change how to think about an emotion eliciting situation to reduce its impact (John &amp; Gross, 2004). There are many different avenues in regards to reappraisals, but the simplest is to find a single positive, no matter how small and remind yourself of it whenever you feel distressed. Instead of ‘The storm destroyed everything’ reframe it as ‘Yes the storm destroyed my home, but my family are alive’.

Socialisation during this phase isn’t just a net positive for teenagers and adults but also young children. A study by La Greca, et al (2013) was conducted looking at children’s distress and recovery trajectories following the devastating Hurricane’s Andrew and Katrina. The study found that overall children experience a similar increase resilience level post-disaster compared to adults; these resilient children in the immediate aftermath of the disaster were encouraged to engage heavily in socialisation. Children that didn’t engage in socialisation developed negative emotional regulation strategies and their recovery trajectory didn’t lend its-self towards resilience. It doesn’t need to be complicated, simply allowing kids to spend time playing with each other has huge benefits on emotional regulation and recovery trajectories. 

If you don’t feel confident being apart of a support group or talking to others, you could also turn to a creative pursuit to vent how you feel. Art is an incredible way of exploring how you feel without the need to meet with others (Reynolds, et al. 2000 ), it doesn’t need to be perfect or complex, a simple pen and paper can do. If your emotions become to intense and upsetting, you could use the creative pursuit to distract yourself from these emotions instead, drawing is considered one of the go to methods of distraction (Dalebroux, Goldstein &amp; Winner, 2008).
[[File:Canberra bushfire memorial-MJC.JPG|thumb|Memorial of the Canberra bushfires]]

==== Reconstruction phase ====
This phase is when you move on from the disaster, moving on doesn’t mean the negative feelings of fear, sadness and anger go away, it simply means they become more manageable. This is a perfect time to engage in community rebuilding pursuits or collective actions to vent any anger at social issues raised by the disaster. Engage in supporting local rebuilding and disaster support groups like the red-cross. You may also want to use the reconstruction as a time to see if a memorial of the disaster and of lives lost will be established. Communities which create  spaces of remembrance often gain a good deal of appreciation, cohesion and acceptance following the disaster (Maddrell &amp; Sidaway, 2010). You could even just organise time with friends and family to conduct your own private acknowledgement of the disaster.   

== Conclusion ==
We have reached the end of our exploration of disasters and emotions, there’s several key take aways I hope you have recognised. The first is that emotions during disasters are not singular, we can experience many emotions over the life-span of the disaster. The next takeaway; in the event of a disaster, you will never be alone in how you feel. In fact there is a high chance you will hold emotions for family members, or find support in dealing with your emotions from those close to you or potentially even from complete strangers. The last takeaway; although disasters have a habit of upheaving our whole life, there is always positive moments to be had. Though I sincerely hope you never experience a natural disaster, if you do, I hope you can recognise why you experience certain emotions and are well equipped to support these emotions to a positive outcome.

==See also==
{{ic|Use bullet points}}

[[Disaster management]]

[[Crisis bonding|Crisis Bonding]]

[[Addiction]]

[[wikipedia:Cognitive_reframing|Cognitive reframing]]

[[wikipedia:Cognitive_reframing|Art Therapy]]

==References==
{{Hanging indent|1=

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Brody, E. M. (2003). Women in the middle: Their parent-care years. Springer Publishing Company.

Cocking, C., Drury, J., &amp; Reicher, S. (2009). The nature of collective resilience: Survivor reactions to the 2005 London bombings. International Journal of Mass Emergencies and Disasters, 27(1), 66-95.

Cvetković, V. M., Öcal, A., &amp; Ivanov, A. (2019). Young adults’ fear of disasters: A case study of residents from Turkey, Serbia and Macedonia. International Journal of Disaster Risk Reduction, 35, 101095. https://doi.org/10.1016/j.ijdrr.2019.101095 

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Eysenck, S. B., Pearson, P. R., Easting, G., &amp; Allsopp, J. F. (1985). Age norms for impulsiveness, venturesomeness and empathy in adults. Personality and individual differences, 6(5), 613-619.

Flory, K., Hankin, B. L., Kloos, B., Cheely, C., &amp; Turecki, G. (2009). Alcohol and cigarette use and misuse among Hurricane Katrina survivors: psychosocial risk and protective factors. Substance use &amp; misuse, 44(12), 1711-1724. https://doi.org/10.3109/10826080902962128

Fredrickson, B. L. (1998). What good are positive emotions?. Review of general psychology, 2(3), 300-319.

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Izard, C. E. (1991). The psychology of emotions. Springer Science &amp; Business Media.

John, O. P., &amp; Gross, J. J. (2004). Healthy and unhealthy emotion regulation: Personality processes, individual differences, and life span development. Journal of personality, 72(6), 1301-1334.

Kako, M., Steenkamp, M., Ryan, B., Arbon, P., &amp; Takada, Y. (2020). Best practice for evacuation centres accommodating vulnerable populations: a literature review. International journal of disaster risk reduction, 46, 101497.

Keltner, D., Ellsworth, P. C., &amp; Edwards, K. (1993). Beyond simple pessimism: effects of sadness and anger on social perception. Journal of personality and social psychology, 64(5), 740.

Kozlowska, K., Walker, P., McLean, L., &amp; Carrive, P. (2015). Fear and the defense cascade: clinical implications and management. Harvard review of psychiatry.

La Greca, A. M., Lai, B. S., Llabre, M. M., Silverman, W. K., Vernberg, E. M., &amp; Prinstein, M. J. (2013, August). Children’s postdisaster trajectories of PTS symptoms: Predicting chronic distress. In Child &amp; youth care forum (Vol. 42, No. 4, pp. 351-369). Springer US.

Lazarus, R. S., &amp; Folkman, S. (1984). Stress, appraisal, and coping. Springer publishing company.

Levenson, R. W. (1999). The intrapersonal functions of emotion. Cognition &amp; Emotion, 13(5), 481-504.

Maddrell, A., &amp; Sidaway, J. D. (Eds.). (2010). Deathscapes: Spaces for death, dying, mourning and remembrance. Ashgate Publishing, Ltd..

Massazza, A., Brewin, C. R., &amp; Joffe, H. (2021). Feelings, thoughts, and behaviors during disaster. Qualitative Health Research, 31(2), 323-337. https://doi.org/10.1177/1049732320968791

Mendon, S., Dutta, P., Behl, A., &amp; Lessmann, S. (2021). A Hybrid approach of machine learning and lexicons to sentiment analysis: enhanced insights from twitter data of natural disasters. Information Systems Frontiers, 23(5), 1145-1168.

Mollaioli, F., AlShawa, O., Liberatore, L., Liberatore, D., &amp; Sorrentino, L. (2019). Seismic demand of the 2016–2017 Central Italy earthquakes. Bulletin of earthquake engineering, 17(10), 5399-5427.

McCorry, L. K. (2007). Physiology of the autonomic nervous system. American journal of pharmaceutical education, 71(4).

Myers, D., &amp; Wee, D. F. (2005). Disaster mental health services. International Journal of Emergency Mental Health, 7(3), 261.

Nuttman-Shwartz, O. (2019). Behavioral responses in youth exposed to natural disasters and political conflict. Current psychiatry reports, 21(6), 1-9.

Öhman, A. (2005). The role of the amygdala in human fear: automatic detection of threat. Psychoneuroendocrinology, 30(10), 953-958.

Reynolds, M. W., Nabors, L., &amp; Quinlan, A. (2000). The effectiveness of art therapy: does it work?. Art Therapy, 17(3), 207-213.

Ross III, D. B., &amp; Coambs, E. (2018). The impact of psychological trauma on finance: Narrative financial therapy considerations in exploring complex trauma and impaired financial decision making. Journal of Financial Therapy.

Sneath, J. Z., Lacey, R., &amp; Kennett-Hensel, P. A. (2009). Coping with a natural disaster: Losses, emotions, and impulsive and compulsive buying. Marketing letters, 20(1), 45-60.

Steimer, T. (2002). The biology of fear-and anxiety-related behaviors. Dialoagues in Clinical Neuroscience, 4 (3), 231-249.

Stephens, A. N., &amp; Groeger, J. A. (2011). Anger-congruent behaviour transfers across driving situations. Cognition &amp; emotion, 25(8), 1423-1438.	https://doi.org/10.1080/02699931.2010.551184

Templeton, A., Guven, S. T., Hoerst, C., Vestergren, S., Davidson, L., Ballentyne, S., ... &amp; Choudhury, S. (2020). Inequalities and identity processes in crises: Recommendations for facilitating safe response to the COVID‐19 pandemic. British Journal of Social Psychology, 59(3), 674-685.

Vandervoort, D. J. (2001). Cross-cultural differences in coping with sadness. Current Psychology, 20(2), 147-153.

Vázquez, C., Cervellón, P., Pérez-Sales, P., Vidales, D., &amp; Gaborit, M. (2005). Positive emotions in earthquake survivors in El Salvador (2001). Journal of Anxiety Disorders, 19(3), 313-328. https://doi.org/10.1016/j.janxdis.2004.03.002

Vestergren, S., Sefa Uysal, M., &amp; Tekin, S. (2022). Do disasters trigger protests? A conceptual view of the connection between disasters, injustice, and protests–the case of COVID-19. Frontiers in Political Science.

World Meteorological Association. (2021, August 31). Weather-related disasters increase over the past 50 years, causing more damage but fewer deaths. [Press release]. https://public.wmo.int/en/media/press-release/weather-related-disasters-increase-over-past-50-years-causing-more-damage-fewer

}}

==External links==
{{ic|Use bullet points}}

[https://public.wmo.int/en/media/press-release/weather-related-disasters-increase-over-past-50-years-causing-more-damage-fewer World Meterological Association press release on increasing natural disasters]

[https://www.redcross.org.au/emergencies/prepare/know/ Red Cross page for being disaster ready]

[https://drinkwise.org.au/#q=alcohol%20and%20your%20health&amp;r=true Drinkwise: limiting consumption of alcohol]

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      <comment>/* Subfamily Bembicinae */  added image</comment>
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      <text bytes="16606" sha1="rua697wf8t1x1i1ubwcwfhwrinxci4v" xml:space="preserve">= Superfamily Apoidea =
== African Ampulicidae ==
&lt;gallery mode=packed heights=150&gt;
Ampulicidae 37894270 suncana.jpg|''Ampulex apicalis''
Dolichurus cf basuto iN 99066897 Sep 29, 2021.jpg|''Dolichurus'' cf ''basuto''
&lt;/gallery&gt;

== African Astatidae ==
&lt;gallery mode=packed heights=150&gt;
Astata iN 105162782 Nicola van Berkel.jpg|''Astata'' sp.
Astata melanaria.jpg|''Astata melanaria''
&lt;/gallery&gt;

== African Bembicidae ==
===Subfamily Bembicinae===	
&lt;gallery mode=packed heights=150&gt;
Bembecinus iN 153052948.jpg|''Bembecinus'' sp.
Bembix iN 195581985.jpg|''Bembix'' sp.
Gorytes natalensis 112517046.jpg|''Gorytes natalensis''
Hoplisoides thalia iN 268375748 a.jpg|''Hoplisoides thalia''
Stizus imperialis.jpg
&lt;/gallery&gt;		
Tribe Gorytini	
*		''Afrogorytes''
*		''Gorytes''
*		''Harpactus''
*		''Hoplisoides''
*		''Lestiphorus''
		
Tribe Spheciini	
*		''Ammatomus''
*		''Kohlia''
*		''Sphecius''
		
Tribe Handlirschiini	
*		''Handlirschia''
		
Tribe Bembicini	
*		''Bembix''
		
Tribe Stizini	
*		''Bembecinus''
*		''Stizoides''
*		''Stizus''

===Subfamily Nyssoninae===	
*		''Brachystegus''
*		''Hovanysson''
*		''Nysson''
		
===Subfamily Alyssontinae===	
*		''Alysson''
*		''Didineis''

== African Crabronidae ==
&lt;gallery mode=packed heights=150&gt;
Dasyproctus iN 30029277 a.jpg
Dicranorhina kohli 2023 07 25 iN 176115975.jpg
Liris on Crassula iN 42678436 01.jpg
Oxybelus iN 250449990 2024 10 09 - 02.jpg
Palarus Bee Pirate iN 144133368 2022-12-01 01.jpg
Paranysson iN 199673489 1.jpg
Pison iN 144131685 2022-11-30 03.jpg
Tachysphex iN 250449986 2024 10 09 7305.jpg
Tachytes iN 188902572 1964.jpg
Trypoxylon iN 99063113 a.jpg
&lt;/gallery&gt;

== African Pemphredonidae ==
&lt;gallery mode=packed heights=150&gt;
Polemistus braunsii iNaturalist 228280708.jpg

&lt;/gallery&gt;

== African Philanthidae ==
&lt;gallery mode=packed heights=150&gt;
Philanthus triangulum diadema 187037342.jpg
Cerceris 2019 12 02 2310.jpg
&lt;/gallery&gt;

== African Psenidae ==
&lt;gallery mode=packed heights=150&gt;
Psenini iN 1022563 i c riddell.jpg

&lt;/gallery&gt;

== African Sphecidae ==
&lt;gallery mode=packed heights=150&gt;
Chalybion 2019 12 02 2314.jpg
Thread-waisted Sand Wasp (Ammophila sp.) carrying a Lienard's Achaea (Achaea lienardi) caterpillar ... (52715218455).jpg
Ammophila ferrugineipes04.jpg
Black Mud-dauber Wasp (Sceliphron spirifex) on Buffalo-Thorn (Ziziphus mucronata) flowers ... (52739846889).jpg
&lt;/gallery&gt;

= Superfamily Chalcidoidea =
 
Chalcidoidea is an incredibly diverse group of wasps with a wide variety of life histories; many are parasitoids, making them ecologically important; some are used for biological control of insect pests. About 22 000 species have been described, but as many as 500 000 are thought to exist worldwide.&lt;ref name=Noyes2019/&gt;

Most chalcidoids are small (body length less than 5 mm), the smallest being males of the mymarid ''Dicopomorpha echmepterygis'', which is the smallest known flying insect (0.13 mm).&lt;ref name=Noyes2019&gt;Noyes, J.S. 2019. Universal Chalcidoidea Database. [http://www.nhm.ac.uk/chalcidoids]&lt;/ref&gt; However, some species may be as long as 20 mm (excluding antennae and ovipositor), such as the pelecinellid ''Doddifoenus wallacei''.&lt;ref name=Krogmann&amp;Burks2009&gt;Krogmann, Lars; Burks, Roger A. (2009-12-31). &quot;Doddifoenus wallacei, a new giant parasitoid wasp of the subfamily Leptofoeninae (Chalcidoidea: Pteromalidae), with a description of its mesosomal skeletal anatomy and a molecular characterization&quot;. Zootaxa. 2194: 21–36. doi:10.5281/zenodo.189452 [https://www.researchgate.net/profile/Lars-Krogmann/publication/250916337 PDF]&lt;/ref&gt; Many have bright metallic colours, hence the name Chalcidoidea or chalcid - the greek word χαλκός (chalcos) means copper or bronze.&lt;ref name=Perseus2023&gt;[http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0073:entry=xalko/s Georg Autenrieth, A Homeric Dictionary]&lt;/ref&gt;

Many new chalcidoid families were proposed in 2022.&lt;ref name=Burks2022&gt;Burks, R., Mitroiu, M.D., Fusu, L., Heraty, J.M., Janšta, P., Heydon, S., Papilloud, N.D.S., Peters, R.S., Tselikh, E.V., Woolley, J.B. and van Noort, S., (2022).﻿ From hell’s heart I stab at thee! A determined approach towards a monophyletic Pteromalidae and reclassification of Chalcidoidea (Hymenoptera). Journal of Hymenoptera Research, 94, pp.13-88. [https://doi.org/10.3897/jhr.94.94263 DOI]&lt;/ref&gt; This was largely based on phylogenetic evidence (both molecular and morphological) accumulated since the families of the Superfamily were outlined in 1993&lt;ref name=Gibson1993&gt;Gibson, G.A.P. (1993) Superfamilies Mymarommatoidea and Chalcidoidea (pp. 570-655). In Goulet, H. &amp; Huber, J. (eds). Hymenoptera of the World: an identification guide to families. Research Branch, Agriculture Canada, Ottawa, Canada, 668 pp. [https://www.researchgate.net/publication/259227143 PDF]&lt;/ref&gt;.


Burks, R., Mitroiu, M.D., Fusu, L., Heraty, J.M., Janšta, P., Heydon, S., Papilloud, N.D.S., Peters, R.S., Tselikh, E.V., Woolley, J.B. and van Noort, S., (2022).﻿ From hell’s heart I stab at thee! A determined approach towards a monophyletic Pteromalidae and reclassification of Chalcidoidea (Hymenoptera). Journal of Hymenoptera Research, 94, pp.13-88. https://doi.org/10.3897/jhr.94.94263

Cruaud, A., Rasplus, J.Y., Zhang, J., Burks, R., Delvare, G., Fusu, L., Gumovsky, A., Huber, J.T., Janšta, P., Mitroiu, M.D. and Noyes, J.S., 2022. The Chalcidoidea bush of life–a massive radiation blurred by mutational saturation. bioRxiv. https://doi.org/10.1101/2022.09.11.507458 https://www.biorxiv.org/content/10.1101/2022.09.11.507458.full.pdf


= Superfamily Ichneumonoidea =

Quicke, D.L., 2015. The braconid and ichneumonid parasitoid wasps: biology, systematics, evolution and ecology. John Wiley &amp; Sons.
https://www.researchgate.net/publication/281662102_The_Braconid_and_Ichneumonid_Parasitoid_Wasps_Biology_Systematics_Evolution_and_Ecology

=== Diplazontinae ===
Quote from Fitton &amp; Rotheray (1982):
&quot;Diplazontines are distinguished easily from other ichneumonids by their general appearance (Fig. 1). The main confirmatory characters are the bifid upper tooth of the mandible (Fig. 2) and the sub-rectangular shape of the first tergite of the gaster (Figs. 1,3,4, 13, 15 and 17). In fact, the diplazontines are so distinct that they can be separated from all other Hymenoptera-Apocrita by possession of the following five characters in combination: (1) antenna of seventeen or more segments (Fig. I); (2) forewing with costal cell obliterated (that is, veins C and Sc + R + Rs contiguous from the wing base to the base of the pterostigma (Fig. 6 ) ; (3) forewing with cross-vein 2 mcu present (Fig. 6); (4) mandible with its upper tooth subdivided (bifid), making the mandible tridentate (Fig. 2); (5) first tergite of gaster sub-rectangular in shape (that is, subequal in width anteriorly and posteriorly) (Figs. 1 , 3 , 4 , 13,15 and 17).&quot;

Fitton, M. G., &amp; Rotheray, G. E. (1982). A key to the European genera of diplazontine ichneumon‐flies, with notes on the British fauna. Systematic Entomology, 7(3), 311-320.

=== Superfamily Pompiloidea ===
Family Mutillidae (Velvet ants)
Family Pompilidae (Spider hunting wasps)
Family Sapygidae (Sapygid wasps)


== Spider-hunting wasps ==
Two wasps from the genus ''Auplopus'' from Europe. Most of the ''Auplopus'' species, along with others from the Tribe Ageniellini, amputate the legs of the spiders they capture; this makes it much easier to move the spider to the nest.
&lt;gallery mode=packed heights=200&gt;
Auplopus carbonarius IMG 1624.jpg
Auplopus carbonarius fg01 20060623 Nied Garten.jpg
&lt;/gallery&gt;
African genera of Ageniellini:
* ''[[Auplopus]]'' &lt;small&gt;Spinola, 1841&lt;/small&gt;
* ''[[Cyemagenia]]'' &lt;small&gt;Arnold, 1946&lt;/small&gt;
* ''[[Dichragenia]]'' &lt;small&gt;Haupt, 1950&lt;/small&gt;
* ''[[Phanagenia]]'' &lt;small&gt;Banks, 1933&lt;/small&gt;   Madagascar
* ''[[Poecilagenia]]'' &lt;small&gt;Haupt, 1926&lt;/small&gt;

== Superfamily Scolioidea ==
=== Family Bradynobaenidae (Bradynobaenid wasps) ===
=== Family Scoliidae (Mammoth wasps) ===

== Superfamily Tiphioidea ==
Family Tiphiidae (Tiphiid wasps)
== Superfamily Thynnoidea ==
Family Thynnidae(Thynnid wasps)
== Superfamily Vespoidea ==
=== Family Rhopalosomatidae (Rhopalosomatid wasps) ===
===Family Vespidae (Paper, Potter &amp; Pollen wasps)===


== '''&lt;big&gt;Hymenoptera&lt;/big&gt;''' ==
About 20 000 described species of [[w:Hymenoptera|Hymenoptera]] (wasps, bees, ants and sawflies) are known from the [[w:Afrotropical|Afrotropical]] region. Estimates of the actual species count for the region range from 100 000 species to as high as 500 000 species.&lt;ref name=WaspWebOverview&gt;[https://www.waspweb.org/Afrotropical_Hymenoptera_book/Background_and_Motivation.htm van Noort, Simon (2023). WaspWeb: Afrotropical Hymenoptera Initiative. www.waspweb.org/Afrotropical_Hymenoptera_book/Background_and_Motivation.htm Retrieved 22 February 2023.]&lt;/ref&gt; Nineteen different superfamilies are illustrated on [[User:Alandmanson/Hymenoptera of southern Africa|this gallery]] in Wikimedia Commons.

The huge number of undescribed species means that many species will be extinct before we are even aware of them, as there are too few taxonomists employed to tackle the task of describing all of them in the next few decades.

==Classification==
The Order can be split into two Suborders - The [[w:Symphyta|Symphyta]] (Woodwasps, Horntails, Sawflies) and the [[w:Apocrita|Apocrita]] (Narrow-waisted wasps, ants and bees).&lt;br&gt;

When compared to the temperate regions of the northern hemisphere, the diversity of Symphyta in Africa is relatively poor, although sawflies of the Superfamily [[w:Tenthredinoidea|Tenthredinoidea]] are fairly common in forests and other woody vegetation types.

Africa has a rich diversity of Apocrita. The cladogram shown below&lt;ref name=Peters&gt;{{Cite journal |last1=Peters |first1=Ralph S. |last2=Krogmann |first2=Lars |last3=Mayer |first3=Christoph |last4=Donath |first4=Alexander |last5=Gunkel |first5=Simon |last6=Meusemann |first6=Karen |last7=Kozlov |first7=Alexey |last8=Podsiadlowski |first8=Lars |last9=Petersen |first9=Malte |title=Evolutionary History of the Hymenoptera |journal=Current Biology |volume=27 |issue=7 |pages=1013–1018 |doi=10.1016/j.cub.2017.01.027|pmid=28343967 |year=2017 |doi-access=free }}&lt;/ref&gt; indicates the possible relationships between 11 of the superfamilies that comprise Apocrita; These 11 superfamilies are all represented in Africa. This breakdown is used by iNaturalist.&lt;ref name=inat-Aculeata&gt;https://www.inaturalist.org/taxa/326777-Aculeata&lt;/ref&gt; It is, however, not accepted by all hymenopterists, and may change as more phylogenetic evidence is accumulated.&lt;ref name=waspwebClass&gt;[https://www.waspweb.org/Classification/index.htm van Noort, Simon (2023). WaspWeb: Classification of Afrotropical Hymenoptera (Wasps, Bees, Ants). www.waspweb.org/Classification/index.htm Retrieved 22 February 2023.]&lt;/ref&gt;
{{Clade|style=font-size:85%; line-height:85%
|label1=Apocrita
            |1={{Clade
               |label1=[[w:Parasitoida|Parasitoida]]
               |1={{Clade
                  |1={{Clade
                     |1=[[w:Ceraphronoidea|Ceraphronoidea]]
                     |2=[[w:Ichneumonoidea|Ichneumonoidea]]
                     }}
                  |label2=[[w:Proctotrupomorpha|Proctotrupomorpha]]
                  |2={{Clade
                     |1=[[w:Cynipoidea|Cynipoidea]]
                     |2={{Clade
                        |1=[[w:Platygastroidea|Platygastroidea]]
                        |2={{Clade
                           |1=[[w:Chalcidoidea|Chalcidoidea]]
                           |2={{Clade
                              |1=[[w:Diaprioidea|Diaprioidea]]
                              |2=[[w:Proctotrupoidea|Proctotrupoidea]]
                  }} }} }} }} }}
               |2={{Clade
                  |1={{Clade
                     |1=[[w:Evanioidea|Evanioidea]]
                     |2=[[w:Stephanoidea|Stephanoidea]]
                     }}
                  |2={{Clade
                     |1=[[w:Trigonaloidea|Trigonaloidea]]
                     |label2=[[w:Aculeata|Aculeata]]
                     |2={{Clade
                        |1=[[w:Chrysidoidea|Chrysidoidea]]
                        |2={{Clade
                           |1=[[w:Vespoidea|Vespoidea]] (potter, honey and social wasps)
                           |2={{Clade
                              |1={{Clade
                                 |1=[[w:Pompiloidea|Pompiloidea]] (velvet ants, spider wasps and relatives)
                                 |2={{Clade
                                    |1=[[w:Thynnoidea|Thynnoidea]]
                                    |2=[[w:Tiphioidea|Tiphioidea]]
                                 }} }}
                              |2={{Clade
                                 |1=[[w:Scolioidea|Scolioidea]]
                                 |2={{Clade
                                    |1=[[w:Formicoidea|Formicoidea]] (ants)
                                    |2=[[w:Apoidea|Apoidea]] (bees and related wasps)
}} }} }} }} }} }} }} }} }}
&lt;br&gt;

==Some common African Symphyta==
&lt;gallery mode=packed heights=200&gt;
Sawfly, Argidae 2021 12 19 12 39 42.jpg|Sawfly, ''Arge'' sp. (Argidae, Superfamily Tenthredinoidea) 
Athalia 2019 11 21 0815.jpg|Sawfly, ''Athalia'' sp. (Tenthredinidae, Superfamily Tenthredinoidea) 
Athalia 2019 08 23 8964.jpg|Sawfly, ''Athalia'' sp. (Tenthredinidae, Superfamily Tenthredinoidea) 
Sirex noctilio F (prof.).JPG|''Sirex noctilio'', a pest in ''Pinus'' plantations (introduced to Africa)&lt;ref name=WaspWebSn&gt;[https://www.waspweb.org/Siricoidea/Siricidae/Sirex/Sirex_noctilio.htm van Noort, Simon (2023). WaspWeb: ''Sirex noctilio''. www.waspweb.org/Classification/index.htm Retrieved 22 February 2023.]&lt;/ref&gt;
&lt;/gallery&gt;

== Frequently reported African Apocrita ==
&lt;br&gt;
[[w:Aculeata|Aculeata]] (ants, bees and stinging wasps) are the most commonly observed Hymenoptera in Africa. There are many more photographs of African Aculeata on the web - See [https://www.waspweb.org/Classification/index.htm African Aculeata on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=326777 African Aculeata on iNaturalist] &lt;br&gt;
&lt;gallery mode=packed heights=200&gt;
Slender Ant (Tetraponera natalensis) (30538051244).jpg|Slender ant (Formicidae, Formicoidea)
Carpenter Bee (Xylocopa inconstans, female) (6021534858).jpg|Female carpenter bee (Apidae, Apoidea)
Chalybion 2019 12 02 2314.jpg|Blue mud-dauber wasp (Sphecidae, Apoidea)
Bethylidae 2019 08 21 13 42 21 8760.jpg|Flat wasp (Bethylidae, Chrysidoidea)
Belonogaster juncea colonialis, manlik, h, Pretoria.jpg|Paper wasp (Vespidae, Vespoidea)
Meria 2020 08 12 2193.jpg|''Meria'' sp. female (Thynnidae, Thynnoidea)
Dasylabris stimulatrix iNat37068107 2019 12 23 2990 W.jpg|''Dasylabris stimulatrix'', a velvet ant (Mutillidae, Pompiloidea)
Pompilidae 2019 05 28 0247.jpg|Spider-hunting wasp (Pompilidae, Pompiloidea)
Scoliid Wasp 2019 06 08 0492.jpg|Campsomerine wasp (Scoliidae, Scolioidea)
&lt;/gallery&gt;&lt;br&gt;

Darwin wasps ([[w:Ichneumonidae|Ichneumonidae]]) and braconids ([[w:Braconidae|Braconidae]]) are also frequently reported. Links to [https://www.waspweb.org/Ichneumonoidea/index.htm African Ichneumonoidea on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=47200 African Ichneumonoidea on iNaturalist].&lt;br&gt;
&lt;gallery mode=packed heights=200&gt;
Echthromorpha agrestoria 2019 10 03 5572.jpg|''Echthromorpha agrestoria'' (Ichneumonidae, Ichneumonoidea)
Ichneumonidae inat 88832241.jpg|''Goryphus tricolor'' (Ichneumonidae, Ichneumonoidea)
Braconid Wasp (Archibracon servillei) (11857083186).jpg|Braconine wasp (Braconidae, Ichneumonoidea) 
2019 09 15 12 55 07 Microgastrinae 38425632.jpg|Microgastrine wasp (Braconidae, Ichneumonoidea) 
&lt;/gallery&gt;&lt;br&gt;

Small [[w:Chalcidoidea|chalcidoid]] parasitic wasps (especially those from the families [[w:Pteromalidae|Pteromalidae]], [[w:Chalcididae|Chalcididae]], [[w:Eulophidae|Eulophidae]], [[w:Eurytomidae|Eurytomidae]]) are also common. Links to [https://www.waspweb.org/Chalcidoidea/index.htm African Chalcidoidea on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=69750 African Chalcidoidea on iNaturalist]
&lt;gallery mode=packed heights=200&gt;
Halticoptera 2019 11 26 2173Cedara.jpg|''Halticoptera'' sp. (Pteromalidae, Chalcidoidea)
Brachymeria 2019 10 09 17 26 38 2520.jpg|''Brachymeria'' sp. (Chalcididae, Chalcidoidea)
Eulophidae Inat 38422095 b.jpg|''Hemiptarsenus'' sp. (Eulophidae, Chalcidoidea)
Eurytomidae00.jpg|Mating seed chalcids (Eurytomidae, Chalcidoidea)
&lt;/gallery&gt;

==References==
{{reflist}}</text>
      <sha1>rua697wf8t1x1i1ubwcwfhwrinxci4v</sha1>
    </revision>
    <revision>
      <id>2815790</id>
      <parentid>2815789</parentid>
      <timestamp>2026-06-15T10:56:26Z</timestamp>
      <contributor>
        <username>Alandmanson</username>
        <id>1669821</id>
      </contributor>
      <comment>/* Subfamily Bembicinae */</comment>
      <origin>2815790</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16628" sha1="67o3mkgrtmydcmer1wqk9mkuenupzbi" xml:space="preserve">= Superfamily Apoidea =
== African Ampulicidae ==
&lt;gallery mode=packed heights=150&gt;
Ampulicidae 37894270 suncana.jpg|''Ampulex apicalis''
Dolichurus cf basuto iN 99066897 Sep 29, 2021.jpg|''Dolichurus'' cf ''basuto''
&lt;/gallery&gt;

== African Astatidae ==
&lt;gallery mode=packed heights=150&gt;
Astata iN 105162782 Nicola van Berkel.jpg|''Astata'' sp.
Astata melanaria.jpg|''Astata melanaria''
&lt;/gallery&gt;

== African Bembicidae ==
===Subfamily Bembicinae===	
&lt;gallery mode=packed heights=150&gt;
Bembecinus iN 153052948.jpg|''Bembecinus'' sp.
Bembix iN 195581985.jpg|''Bembix'' sp.
Gorytes natalensis 112517046.jpg|''Gorytes natalensis''
Hoplisoides thalia iN 268375748 a.jpg|''Hoplisoides thalia''
Stizus imperialis.jpg|''Stizus imperialis''
&lt;/gallery&gt;		
Tribe Gorytini	
*		''Afrogorytes''
*		''Gorytes''
*		''Harpactus''
*		''Hoplisoides''
*		''Lestiphorus''
		
Tribe Spheciini	
*		''Ammatomus''
*		''Kohlia''
*		''Sphecius''
		
Tribe Handlirschiini	
*		''Handlirschia''
		
Tribe Bembicini	
*		''Bembix''
		
Tribe Stizini	
*		''Bembecinus''
*		''Stizoides''
*		''Stizus''

===Subfamily Nyssoninae===	
*		''Brachystegus''
*		''Hovanysson''
*		''Nysson''
		
===Subfamily Alyssontinae===	
*		''Alysson''
*		''Didineis''

== African Crabronidae ==
&lt;gallery mode=packed heights=150&gt;
Dasyproctus iN 30029277 a.jpg
Dicranorhina kohli 2023 07 25 iN 176115975.jpg
Liris on Crassula iN 42678436 01.jpg
Oxybelus iN 250449990 2024 10 09 - 02.jpg
Palarus Bee Pirate iN 144133368 2022-12-01 01.jpg
Paranysson iN 199673489 1.jpg
Pison iN 144131685 2022-11-30 03.jpg
Tachysphex iN 250449986 2024 10 09 7305.jpg
Tachytes iN 188902572 1964.jpg
Trypoxylon iN 99063113 a.jpg
&lt;/gallery&gt;

== African Pemphredonidae ==
&lt;gallery mode=packed heights=150&gt;
Polemistus braunsii iNaturalist 228280708.jpg

&lt;/gallery&gt;

== African Philanthidae ==
&lt;gallery mode=packed heights=150&gt;
Philanthus triangulum diadema 187037342.jpg
Cerceris 2019 12 02 2310.jpg
&lt;/gallery&gt;

== African Psenidae ==
&lt;gallery mode=packed heights=150&gt;
Psenini iN 1022563 i c riddell.jpg

&lt;/gallery&gt;

== African Sphecidae ==
&lt;gallery mode=packed heights=150&gt;
Chalybion 2019 12 02 2314.jpg
Thread-waisted Sand Wasp (Ammophila sp.) carrying a Lienard's Achaea (Achaea lienardi) caterpillar ... (52715218455).jpg
Ammophila ferrugineipes04.jpg
Black Mud-dauber Wasp (Sceliphron spirifex) on Buffalo-Thorn (Ziziphus mucronata) flowers ... (52739846889).jpg
&lt;/gallery&gt;

= Superfamily Chalcidoidea =
 
Chalcidoidea is an incredibly diverse group of wasps with a wide variety of life histories; many are parasitoids, making them ecologically important; some are used for biological control of insect pests. About 22 000 species have been described, but as many as 500 000 are thought to exist worldwide.&lt;ref name=Noyes2019/&gt;

Most chalcidoids are small (body length less than 5 mm), the smallest being males of the mymarid ''Dicopomorpha echmepterygis'', which is the smallest known flying insect (0.13 mm).&lt;ref name=Noyes2019&gt;Noyes, J.S. 2019. Universal Chalcidoidea Database. [http://www.nhm.ac.uk/chalcidoids]&lt;/ref&gt; However, some species may be as long as 20 mm (excluding antennae and ovipositor), such as the pelecinellid ''Doddifoenus wallacei''.&lt;ref name=Krogmann&amp;Burks2009&gt;Krogmann, Lars; Burks, Roger A. (2009-12-31). &quot;Doddifoenus wallacei, a new giant parasitoid wasp of the subfamily Leptofoeninae (Chalcidoidea: Pteromalidae), with a description of its mesosomal skeletal anatomy and a molecular characterization&quot;. Zootaxa. 2194: 21–36. doi:10.5281/zenodo.189452 [https://www.researchgate.net/profile/Lars-Krogmann/publication/250916337 PDF]&lt;/ref&gt; Many have bright metallic colours, hence the name Chalcidoidea or chalcid - the greek word χαλκός (chalcos) means copper or bronze.&lt;ref name=Perseus2023&gt;[http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0073:entry=xalko/s Georg Autenrieth, A Homeric Dictionary]&lt;/ref&gt;

Many new chalcidoid families were proposed in 2022.&lt;ref name=Burks2022&gt;Burks, R., Mitroiu, M.D., Fusu, L., Heraty, J.M., Janšta, P., Heydon, S., Papilloud, N.D.S., Peters, R.S., Tselikh, E.V., Woolley, J.B. and van Noort, S., (2022).﻿ From hell’s heart I stab at thee! A determined approach towards a monophyletic Pteromalidae and reclassification of Chalcidoidea (Hymenoptera). Journal of Hymenoptera Research, 94, pp.13-88. [https://doi.org/10.3897/jhr.94.94263 DOI]&lt;/ref&gt; This was largely based on phylogenetic evidence (both molecular and morphological) accumulated since the families of the Superfamily were outlined in 1993&lt;ref name=Gibson1993&gt;Gibson, G.A.P. (1993) Superfamilies Mymarommatoidea and Chalcidoidea (pp. 570-655). In Goulet, H. &amp; Huber, J. (eds). Hymenoptera of the World: an identification guide to families. Research Branch, Agriculture Canada, Ottawa, Canada, 668 pp. [https://www.researchgate.net/publication/259227143 PDF]&lt;/ref&gt;.


Burks, R., Mitroiu, M.D., Fusu, L., Heraty, J.M., Janšta, P., Heydon, S., Papilloud, N.D.S., Peters, R.S., Tselikh, E.V., Woolley, J.B. and van Noort, S., (2022).﻿ From hell’s heart I stab at thee! A determined approach towards a monophyletic Pteromalidae and reclassification of Chalcidoidea (Hymenoptera). Journal of Hymenoptera Research, 94, pp.13-88. https://doi.org/10.3897/jhr.94.94263

Cruaud, A., Rasplus, J.Y., Zhang, J., Burks, R., Delvare, G., Fusu, L., Gumovsky, A., Huber, J.T., Janšta, P., Mitroiu, M.D. and Noyes, J.S., 2022. The Chalcidoidea bush of life–a massive radiation blurred by mutational saturation. bioRxiv. https://doi.org/10.1101/2022.09.11.507458 https://www.biorxiv.org/content/10.1101/2022.09.11.507458.full.pdf


= Superfamily Ichneumonoidea =

Quicke, D.L., 2015. The braconid and ichneumonid parasitoid wasps: biology, systematics, evolution and ecology. John Wiley &amp; Sons.
https://www.researchgate.net/publication/281662102_The_Braconid_and_Ichneumonid_Parasitoid_Wasps_Biology_Systematics_Evolution_and_Ecology

=== Diplazontinae ===
Quote from Fitton &amp; Rotheray (1982):
&quot;Diplazontines are distinguished easily from other ichneumonids by their general appearance (Fig. 1). The main confirmatory characters are the bifid upper tooth of the mandible (Fig. 2) and the sub-rectangular shape of the first tergite of the gaster (Figs. 1,3,4, 13, 15 and 17). In fact, the diplazontines are so distinct that they can be separated from all other Hymenoptera-Apocrita by possession of the following five characters in combination: (1) antenna of seventeen or more segments (Fig. I); (2) forewing with costal cell obliterated (that is, veins C and Sc + R + Rs contiguous from the wing base to the base of the pterostigma (Fig. 6 ) ; (3) forewing with cross-vein 2 mcu present (Fig. 6); (4) mandible with its upper tooth subdivided (bifid), making the mandible tridentate (Fig. 2); (5) first tergite of gaster sub-rectangular in shape (that is, subequal in width anteriorly and posteriorly) (Figs. 1 , 3 , 4 , 13,15 and 17).&quot;

Fitton, M. G., &amp; Rotheray, G. E. (1982). A key to the European genera of diplazontine ichneumon‐flies, with notes on the British fauna. Systematic Entomology, 7(3), 311-320.

=== Superfamily Pompiloidea ===
Family Mutillidae (Velvet ants)
Family Pompilidae (Spider hunting wasps)
Family Sapygidae (Sapygid wasps)


== Spider-hunting wasps ==
Two wasps from the genus ''Auplopus'' from Europe. Most of the ''Auplopus'' species, along with others from the Tribe Ageniellini, amputate the legs of the spiders they capture; this makes it much easier to move the spider to the nest.
&lt;gallery mode=packed heights=200&gt;
Auplopus carbonarius IMG 1624.jpg
Auplopus carbonarius fg01 20060623 Nied Garten.jpg
&lt;/gallery&gt;
African genera of Ageniellini:
* ''[[Auplopus]]'' &lt;small&gt;Spinola, 1841&lt;/small&gt;
* ''[[Cyemagenia]]'' &lt;small&gt;Arnold, 1946&lt;/small&gt;
* ''[[Dichragenia]]'' &lt;small&gt;Haupt, 1950&lt;/small&gt;
* ''[[Phanagenia]]'' &lt;small&gt;Banks, 1933&lt;/small&gt;   Madagascar
* ''[[Poecilagenia]]'' &lt;small&gt;Haupt, 1926&lt;/small&gt;

== Superfamily Scolioidea ==
=== Family Bradynobaenidae (Bradynobaenid wasps) ===
=== Family Scoliidae (Mammoth wasps) ===

== Superfamily Tiphioidea ==
Family Tiphiidae (Tiphiid wasps)
== Superfamily Thynnoidea ==
Family Thynnidae(Thynnid wasps)
== Superfamily Vespoidea ==
=== Family Rhopalosomatidae (Rhopalosomatid wasps) ===
===Family Vespidae (Paper, Potter &amp; Pollen wasps)===


== '''&lt;big&gt;Hymenoptera&lt;/big&gt;''' ==
About 20 000 described species of [[w:Hymenoptera|Hymenoptera]] (wasps, bees, ants and sawflies) are known from the [[w:Afrotropical|Afrotropical]] region. Estimates of the actual species count for the region range from 100 000 species to as high as 500 000 species.&lt;ref name=WaspWebOverview&gt;[https://www.waspweb.org/Afrotropical_Hymenoptera_book/Background_and_Motivation.htm van Noort, Simon (2023). WaspWeb: Afrotropical Hymenoptera Initiative. www.waspweb.org/Afrotropical_Hymenoptera_book/Background_and_Motivation.htm Retrieved 22 February 2023.]&lt;/ref&gt; Nineteen different superfamilies are illustrated on [[User:Alandmanson/Hymenoptera of southern Africa|this gallery]] in Wikimedia Commons.

The huge number of undescribed species means that many species will be extinct before we are even aware of them, as there are too few taxonomists employed to tackle the task of describing all of them in the next few decades.

==Classification==
The Order can be split into two Suborders - The [[w:Symphyta|Symphyta]] (Woodwasps, Horntails, Sawflies) and the [[w:Apocrita|Apocrita]] (Narrow-waisted wasps, ants and bees).&lt;br&gt;

When compared to the temperate regions of the northern hemisphere, the diversity of Symphyta in Africa is relatively poor, although sawflies of the Superfamily [[w:Tenthredinoidea|Tenthredinoidea]] are fairly common in forests and other woody vegetation types.

Africa has a rich diversity of Apocrita. The cladogram shown below&lt;ref name=Peters&gt;{{Cite journal |last1=Peters |first1=Ralph S. |last2=Krogmann |first2=Lars |last3=Mayer |first3=Christoph |last4=Donath |first4=Alexander |last5=Gunkel |first5=Simon |last6=Meusemann |first6=Karen |last7=Kozlov |first7=Alexey |last8=Podsiadlowski |first8=Lars |last9=Petersen |first9=Malte |title=Evolutionary History of the Hymenoptera |journal=Current Biology |volume=27 |issue=7 |pages=1013–1018 |doi=10.1016/j.cub.2017.01.027|pmid=28343967 |year=2017 |doi-access=free }}&lt;/ref&gt; indicates the possible relationships between 11 of the superfamilies that comprise Apocrita; These 11 superfamilies are all represented in Africa. This breakdown is used by iNaturalist.&lt;ref name=inat-Aculeata&gt;https://www.inaturalist.org/taxa/326777-Aculeata&lt;/ref&gt; It is, however, not accepted by all hymenopterists, and may change as more phylogenetic evidence is accumulated.&lt;ref name=waspwebClass&gt;[https://www.waspweb.org/Classification/index.htm van Noort, Simon (2023). WaspWeb: Classification of Afrotropical Hymenoptera (Wasps, Bees, Ants). www.waspweb.org/Classification/index.htm Retrieved 22 February 2023.]&lt;/ref&gt;
{{Clade|style=font-size:85%; line-height:85%
|label1=Apocrita
            |1={{Clade
               |label1=[[w:Parasitoida|Parasitoida]]
               |1={{Clade
                  |1={{Clade
                     |1=[[w:Ceraphronoidea|Ceraphronoidea]]
                     |2=[[w:Ichneumonoidea|Ichneumonoidea]]
                     }}
                  |label2=[[w:Proctotrupomorpha|Proctotrupomorpha]]
                  |2={{Clade
                     |1=[[w:Cynipoidea|Cynipoidea]]
                     |2={{Clade
                        |1=[[w:Platygastroidea|Platygastroidea]]
                        |2={{Clade
                           |1=[[w:Chalcidoidea|Chalcidoidea]]
                           |2={{Clade
                              |1=[[w:Diaprioidea|Diaprioidea]]
                              |2=[[w:Proctotrupoidea|Proctotrupoidea]]
                  }} }} }} }} }}
               |2={{Clade
                  |1={{Clade
                     |1=[[w:Evanioidea|Evanioidea]]
                     |2=[[w:Stephanoidea|Stephanoidea]]
                     }}
                  |2={{Clade
                     |1=[[w:Trigonaloidea|Trigonaloidea]]
                     |label2=[[w:Aculeata|Aculeata]]
                     |2={{Clade
                        |1=[[w:Chrysidoidea|Chrysidoidea]]
                        |2={{Clade
                           |1=[[w:Vespoidea|Vespoidea]] (potter, honey and social wasps)
                           |2={{Clade
                              |1={{Clade
                                 |1=[[w:Pompiloidea|Pompiloidea]] (velvet ants, spider wasps and relatives)
                                 |2={{Clade
                                    |1=[[w:Thynnoidea|Thynnoidea]]
                                    |2=[[w:Tiphioidea|Tiphioidea]]
                                 }} }}
                              |2={{Clade
                                 |1=[[w:Scolioidea|Scolioidea]]
                                 |2={{Clade
                                    |1=[[w:Formicoidea|Formicoidea]] (ants)
                                    |2=[[w:Apoidea|Apoidea]] (bees and related wasps)
}} }} }} }} }} }} }} }} }}
&lt;br&gt;

==Some common African Symphyta==
&lt;gallery mode=packed heights=200&gt;
Sawfly, Argidae 2021 12 19 12 39 42.jpg|Sawfly, ''Arge'' sp. (Argidae, Superfamily Tenthredinoidea) 
Athalia 2019 11 21 0815.jpg|Sawfly, ''Athalia'' sp. (Tenthredinidae, Superfamily Tenthredinoidea) 
Athalia 2019 08 23 8964.jpg|Sawfly, ''Athalia'' sp. (Tenthredinidae, Superfamily Tenthredinoidea) 
Sirex noctilio F (prof.).JPG|''Sirex noctilio'', a pest in ''Pinus'' plantations (introduced to Africa)&lt;ref name=WaspWebSn&gt;[https://www.waspweb.org/Siricoidea/Siricidae/Sirex/Sirex_noctilio.htm van Noort, Simon (2023). WaspWeb: ''Sirex noctilio''. www.waspweb.org/Classification/index.htm Retrieved 22 February 2023.]&lt;/ref&gt;
&lt;/gallery&gt;

== Frequently reported African Apocrita ==
&lt;br&gt;
[[w:Aculeata|Aculeata]] (ants, bees and stinging wasps) are the most commonly observed Hymenoptera in Africa. There are many more photographs of African Aculeata on the web - See [https://www.waspweb.org/Classification/index.htm African Aculeata on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=326777 African Aculeata on iNaturalist] &lt;br&gt;
&lt;gallery mode=packed heights=200&gt;
Slender Ant (Tetraponera natalensis) (30538051244).jpg|Slender ant (Formicidae, Formicoidea)
Carpenter Bee (Xylocopa inconstans, female) (6021534858).jpg|Female carpenter bee (Apidae, Apoidea)
Chalybion 2019 12 02 2314.jpg|Blue mud-dauber wasp (Sphecidae, Apoidea)
Bethylidae 2019 08 21 13 42 21 8760.jpg|Flat wasp (Bethylidae, Chrysidoidea)
Belonogaster juncea colonialis, manlik, h, Pretoria.jpg|Paper wasp (Vespidae, Vespoidea)
Meria 2020 08 12 2193.jpg|''Meria'' sp. female (Thynnidae, Thynnoidea)
Dasylabris stimulatrix iNat37068107 2019 12 23 2990 W.jpg|''Dasylabris stimulatrix'', a velvet ant (Mutillidae, Pompiloidea)
Pompilidae 2019 05 28 0247.jpg|Spider-hunting wasp (Pompilidae, Pompiloidea)
Scoliid Wasp 2019 06 08 0492.jpg|Campsomerine wasp (Scoliidae, Scolioidea)
&lt;/gallery&gt;&lt;br&gt;

Darwin wasps ([[w:Ichneumonidae|Ichneumonidae]]) and braconids ([[w:Braconidae|Braconidae]]) are also frequently reported. Links to [https://www.waspweb.org/Ichneumonoidea/index.htm African Ichneumonoidea on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=47200 African Ichneumonoidea on iNaturalist].&lt;br&gt;
&lt;gallery mode=packed heights=200&gt;
Echthromorpha agrestoria 2019 10 03 5572.jpg|''Echthromorpha agrestoria'' (Ichneumonidae, Ichneumonoidea)
Ichneumonidae inat 88832241.jpg|''Goryphus tricolor'' (Ichneumonidae, Ichneumonoidea)
Braconid Wasp (Archibracon servillei) (11857083186).jpg|Braconine wasp (Braconidae, Ichneumonoidea) 
2019 09 15 12 55 07 Microgastrinae 38425632.jpg|Microgastrine wasp (Braconidae, Ichneumonoidea) 
&lt;/gallery&gt;&lt;br&gt;

Small [[w:Chalcidoidea|chalcidoid]] parasitic wasps (especially those from the families [[w:Pteromalidae|Pteromalidae]], [[w:Chalcididae|Chalcididae]], [[w:Eulophidae|Eulophidae]], [[w:Eurytomidae|Eurytomidae]]) are also common. Links to [https://www.waspweb.org/Chalcidoidea/index.htm African Chalcidoidea on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=69750 African Chalcidoidea on iNaturalist]
&lt;gallery mode=packed heights=200&gt;
Halticoptera 2019 11 26 2173Cedara.jpg|''Halticoptera'' sp. (Pteromalidae, Chalcidoidea)
Brachymeria 2019 10 09 17 26 38 2520.jpg|''Brachymeria'' sp. (Chalcididae, Chalcidoidea)
Eulophidae Inat 38422095 b.jpg|''Hemiptarsenus'' sp. (Eulophidae, Chalcidoidea)
Eurytomidae00.jpg|Mating seed chalcids (Eurytomidae, Chalcidoidea)
&lt;/gallery&gt;

==References==
{{reflist}}</text>
      <sha1>67o3mkgrtmydcmer1wqk9mkuenupzbi</sha1>
    </revision>
    <revision>
      <id>2815791</id>
      <parentid>2815790</parentid>
      <timestamp>2026-06-15T11:04:05Z</timestamp>
      <contributor>
        <username>Alandmanson</username>
        <id>1669821</id>
      </contributor>
      <comment>/* Subfamily Bembicinae */</comment>
      <origin>2815791</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16686" sha1="1xbkj2kj4r4c3ruh7kamkc3nj522me6" xml:space="preserve">= Superfamily Apoidea =
== African Ampulicidae ==
&lt;gallery mode=packed heights=150&gt;
Ampulicidae 37894270 suncana.jpg|''Ampulex apicalis''
Dolichurus cf basuto iN 99066897 Sep 29, 2021.jpg|''Dolichurus'' cf ''basuto''
&lt;/gallery&gt;

== African Astatidae ==
&lt;gallery mode=packed heights=150&gt;
Astata iN 105162782 Nicola van Berkel.jpg|''Astata'' sp.
Astata melanaria.jpg|''Astata melanaria''
&lt;/gallery&gt;

== African Bembicidae ==
===Subfamily Bembicinae===	
&lt;gallery mode=packed heights=150&gt;
Bembecinus iN 153052948.jpg|''Bembecinus'' sp.
Bembix iN 195581985.jpg|''Bembix'' sp.
Gorytes natalensis 112517046.jpg|''Gorytes natalensis''
Hoplisoides thalia iN 268375748 a.jpg|''Hoplisoides thalia''
Sand wasp (Stizus fuscipennis).jpg|''Stizus fuscipennis''
Stizus imperialis.jpg|''Stizus imperialis''
&lt;/gallery&gt;		
Tribe Gorytini	
*		''Afrogorytes''
*		''Gorytes''
*		''Harpactus''
*		''Hoplisoides''
*		''Lestiphorus''
		
Tribe Spheciini	
*		''Ammatomus''
*		''Kohlia''
*		''Sphecius''
		
Tribe Handlirschiini	
*		''Handlirschia''
		
Tribe Bembicini	
*		''Bembix''
		
Tribe Stizini	
*		''Bembecinus''
*		''Stizoides''
*		''Stizus''

===Subfamily Nyssoninae===	
*		''Brachystegus''
*		''Hovanysson''
*		''Nysson''
		
===Subfamily Alyssontinae===	
*		''Alysson''
*		''Didineis''

== African Crabronidae ==
&lt;gallery mode=packed heights=150&gt;
Dasyproctus iN 30029277 a.jpg
Dicranorhina kohli 2023 07 25 iN 176115975.jpg
Liris on Crassula iN 42678436 01.jpg
Oxybelus iN 250449990 2024 10 09 - 02.jpg
Palarus Bee Pirate iN 144133368 2022-12-01 01.jpg
Paranysson iN 199673489 1.jpg
Pison iN 144131685 2022-11-30 03.jpg
Tachysphex iN 250449986 2024 10 09 7305.jpg
Tachytes iN 188902572 1964.jpg
Trypoxylon iN 99063113 a.jpg
&lt;/gallery&gt;

== African Pemphredonidae ==
&lt;gallery mode=packed heights=150&gt;
Polemistus braunsii iNaturalist 228280708.jpg

&lt;/gallery&gt;

== African Philanthidae ==
&lt;gallery mode=packed heights=150&gt;
Philanthus triangulum diadema 187037342.jpg
Cerceris 2019 12 02 2310.jpg
&lt;/gallery&gt;

== African Psenidae ==
&lt;gallery mode=packed heights=150&gt;
Psenini iN 1022563 i c riddell.jpg

&lt;/gallery&gt;

== African Sphecidae ==
&lt;gallery mode=packed heights=150&gt;
Chalybion 2019 12 02 2314.jpg
Thread-waisted Sand Wasp (Ammophila sp.) carrying a Lienard's Achaea (Achaea lienardi) caterpillar ... (52715218455).jpg
Ammophila ferrugineipes04.jpg
Black Mud-dauber Wasp (Sceliphron spirifex) on Buffalo-Thorn (Ziziphus mucronata) flowers ... (52739846889).jpg
&lt;/gallery&gt;

= Superfamily Chalcidoidea =
 
Chalcidoidea is an incredibly diverse group of wasps with a wide variety of life histories; many are parasitoids, making them ecologically important; some are used for biological control of insect pests. About 22 000 species have been described, but as many as 500 000 are thought to exist worldwide.&lt;ref name=Noyes2019/&gt;

Most chalcidoids are small (body length less than 5 mm), the smallest being males of the mymarid ''Dicopomorpha echmepterygis'', which is the smallest known flying insect (0.13 mm).&lt;ref name=Noyes2019&gt;Noyes, J.S. 2019. Universal Chalcidoidea Database. [http://www.nhm.ac.uk/chalcidoids]&lt;/ref&gt; However, some species may be as long as 20 mm (excluding antennae and ovipositor), such as the pelecinellid ''Doddifoenus wallacei''.&lt;ref name=Krogmann&amp;Burks2009&gt;Krogmann, Lars; Burks, Roger A. (2009-12-31). &quot;Doddifoenus wallacei, a new giant parasitoid wasp of the subfamily Leptofoeninae (Chalcidoidea: Pteromalidae), with a description of its mesosomal skeletal anatomy and a molecular characterization&quot;. Zootaxa. 2194: 21–36. doi:10.5281/zenodo.189452 [https://www.researchgate.net/profile/Lars-Krogmann/publication/250916337 PDF]&lt;/ref&gt; Many have bright metallic colours, hence the name Chalcidoidea or chalcid - the greek word χαλκός (chalcos) means copper or bronze.&lt;ref name=Perseus2023&gt;[http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0073:entry=xalko/s Georg Autenrieth, A Homeric Dictionary]&lt;/ref&gt;

Many new chalcidoid families were proposed in 2022.&lt;ref name=Burks2022&gt;Burks, R., Mitroiu, M.D., Fusu, L., Heraty, J.M., Janšta, P., Heydon, S., Papilloud, N.D.S., Peters, R.S., Tselikh, E.V., Woolley, J.B. and van Noort, S., (2022).﻿ From hell’s heart I stab at thee! A determined approach towards a monophyletic Pteromalidae and reclassification of Chalcidoidea (Hymenoptera). Journal of Hymenoptera Research, 94, pp.13-88. [https://doi.org/10.3897/jhr.94.94263 DOI]&lt;/ref&gt; This was largely based on phylogenetic evidence (both molecular and morphological) accumulated since the families of the Superfamily were outlined in 1993&lt;ref name=Gibson1993&gt;Gibson, G.A.P. (1993) Superfamilies Mymarommatoidea and Chalcidoidea (pp. 570-655). In Goulet, H. &amp; Huber, J. (eds). Hymenoptera of the World: an identification guide to families. Research Branch, Agriculture Canada, Ottawa, Canada, 668 pp. [https://www.researchgate.net/publication/259227143 PDF]&lt;/ref&gt;.


Burks, R., Mitroiu, M.D., Fusu, L., Heraty, J.M., Janšta, P., Heydon, S., Papilloud, N.D.S., Peters, R.S., Tselikh, E.V., Woolley, J.B. and van Noort, S., (2022).﻿ From hell’s heart I stab at thee! A determined approach towards a monophyletic Pteromalidae and reclassification of Chalcidoidea (Hymenoptera). Journal of Hymenoptera Research, 94, pp.13-88. https://doi.org/10.3897/jhr.94.94263

Cruaud, A., Rasplus, J.Y., Zhang, J., Burks, R., Delvare, G., Fusu, L., Gumovsky, A., Huber, J.T., Janšta, P., Mitroiu, M.D. and Noyes, J.S., 2022. The Chalcidoidea bush of life–a massive radiation blurred by mutational saturation. bioRxiv. https://doi.org/10.1101/2022.09.11.507458 https://www.biorxiv.org/content/10.1101/2022.09.11.507458.full.pdf


= Superfamily Ichneumonoidea =

Quicke, D.L., 2015. The braconid and ichneumonid parasitoid wasps: biology, systematics, evolution and ecology. John Wiley &amp; Sons.
https://www.researchgate.net/publication/281662102_The_Braconid_and_Ichneumonid_Parasitoid_Wasps_Biology_Systematics_Evolution_and_Ecology

=== Diplazontinae ===
Quote from Fitton &amp; Rotheray (1982):
&quot;Diplazontines are distinguished easily from other ichneumonids by their general appearance (Fig. 1). The main confirmatory characters are the bifid upper tooth of the mandible (Fig. 2) and the sub-rectangular shape of the first tergite of the gaster (Figs. 1,3,4, 13, 15 and 17). In fact, the diplazontines are so distinct that they can be separated from all other Hymenoptera-Apocrita by possession of the following five characters in combination: (1) antenna of seventeen or more segments (Fig. I); (2) forewing with costal cell obliterated (that is, veins C and Sc + R + Rs contiguous from the wing base to the base of the pterostigma (Fig. 6 ) ; (3) forewing with cross-vein 2 mcu present (Fig. 6); (4) mandible with its upper tooth subdivided (bifid), making the mandible tridentate (Fig. 2); (5) first tergite of gaster sub-rectangular in shape (that is, subequal in width anteriorly and posteriorly) (Figs. 1 , 3 , 4 , 13,15 and 17).&quot;

Fitton, M. G., &amp; Rotheray, G. E. (1982). A key to the European genera of diplazontine ichneumon‐flies, with notes on the British fauna. Systematic Entomology, 7(3), 311-320.

=== Superfamily Pompiloidea ===
Family Mutillidae (Velvet ants)
Family Pompilidae (Spider hunting wasps)
Family Sapygidae (Sapygid wasps)


== Spider-hunting wasps ==
Two wasps from the genus ''Auplopus'' from Europe. Most of the ''Auplopus'' species, along with others from the Tribe Ageniellini, amputate the legs of the spiders they capture; this makes it much easier to move the spider to the nest.
&lt;gallery mode=packed heights=200&gt;
Auplopus carbonarius IMG 1624.jpg
Auplopus carbonarius fg01 20060623 Nied Garten.jpg
&lt;/gallery&gt;
African genera of Ageniellini:
* ''[[Auplopus]]'' &lt;small&gt;Spinola, 1841&lt;/small&gt;
* ''[[Cyemagenia]]'' &lt;small&gt;Arnold, 1946&lt;/small&gt;
* ''[[Dichragenia]]'' &lt;small&gt;Haupt, 1950&lt;/small&gt;
* ''[[Phanagenia]]'' &lt;small&gt;Banks, 1933&lt;/small&gt;   Madagascar
* ''[[Poecilagenia]]'' &lt;small&gt;Haupt, 1926&lt;/small&gt;

== Superfamily Scolioidea ==
=== Family Bradynobaenidae (Bradynobaenid wasps) ===
=== Family Scoliidae (Mammoth wasps) ===

== Superfamily Tiphioidea ==
Family Tiphiidae (Tiphiid wasps)
== Superfamily Thynnoidea ==
Family Thynnidae(Thynnid wasps)
== Superfamily Vespoidea ==
=== Family Rhopalosomatidae (Rhopalosomatid wasps) ===
===Family Vespidae (Paper, Potter &amp; Pollen wasps)===


== '''&lt;big&gt;Hymenoptera&lt;/big&gt;''' ==
About 20 000 described species of [[w:Hymenoptera|Hymenoptera]] (wasps, bees, ants and sawflies) are known from the [[w:Afrotropical|Afrotropical]] region. Estimates of the actual species count for the region range from 100 000 species to as high as 500 000 species.&lt;ref name=WaspWebOverview&gt;[https://www.waspweb.org/Afrotropical_Hymenoptera_book/Background_and_Motivation.htm van Noort, Simon (2023). WaspWeb: Afrotropical Hymenoptera Initiative. www.waspweb.org/Afrotropical_Hymenoptera_book/Background_and_Motivation.htm Retrieved 22 February 2023.]&lt;/ref&gt; Nineteen different superfamilies are illustrated on [[User:Alandmanson/Hymenoptera of southern Africa|this gallery]] in Wikimedia Commons.

The huge number of undescribed species means that many species will be extinct before we are even aware of them, as there are too few taxonomists employed to tackle the task of describing all of them in the next few decades.

==Classification==
The Order can be split into two Suborders - The [[w:Symphyta|Symphyta]] (Woodwasps, Horntails, Sawflies) and the [[w:Apocrita|Apocrita]] (Narrow-waisted wasps, ants and bees).&lt;br&gt;

When compared to the temperate regions of the northern hemisphere, the diversity of Symphyta in Africa is relatively poor, although sawflies of the Superfamily [[w:Tenthredinoidea|Tenthredinoidea]] are fairly common in forests and other woody vegetation types.

Africa has a rich diversity of Apocrita. The cladogram shown below&lt;ref name=Peters&gt;{{Cite journal |last1=Peters |first1=Ralph S. |last2=Krogmann |first2=Lars |last3=Mayer |first3=Christoph |last4=Donath |first4=Alexander |last5=Gunkel |first5=Simon |last6=Meusemann |first6=Karen |last7=Kozlov |first7=Alexey |last8=Podsiadlowski |first8=Lars |last9=Petersen |first9=Malte |title=Evolutionary History of the Hymenoptera |journal=Current Biology |volume=27 |issue=7 |pages=1013–1018 |doi=10.1016/j.cub.2017.01.027|pmid=28343967 |year=2017 |doi-access=free }}&lt;/ref&gt; indicates the possible relationships between 11 of the superfamilies that comprise Apocrita; These 11 superfamilies are all represented in Africa. This breakdown is used by iNaturalist.&lt;ref name=inat-Aculeata&gt;https://www.inaturalist.org/taxa/326777-Aculeata&lt;/ref&gt; It is, however, not accepted by all hymenopterists, and may change as more phylogenetic evidence is accumulated.&lt;ref name=waspwebClass&gt;[https://www.waspweb.org/Classification/index.htm van Noort, Simon (2023). WaspWeb: Classification of Afrotropical Hymenoptera (Wasps, Bees, Ants). www.waspweb.org/Classification/index.htm Retrieved 22 February 2023.]&lt;/ref&gt;
{{Clade|style=font-size:85%; line-height:85%
|label1=Apocrita
            |1={{Clade
               |label1=[[w:Parasitoida|Parasitoida]]
               |1={{Clade
                  |1={{Clade
                     |1=[[w:Ceraphronoidea|Ceraphronoidea]]
                     |2=[[w:Ichneumonoidea|Ichneumonoidea]]
                     }}
                  |label2=[[w:Proctotrupomorpha|Proctotrupomorpha]]
                  |2={{Clade
                     |1=[[w:Cynipoidea|Cynipoidea]]
                     |2={{Clade
                        |1=[[w:Platygastroidea|Platygastroidea]]
                        |2={{Clade
                           |1=[[w:Chalcidoidea|Chalcidoidea]]
                           |2={{Clade
                              |1=[[w:Diaprioidea|Diaprioidea]]
                              |2=[[w:Proctotrupoidea|Proctotrupoidea]]
                  }} }} }} }} }}
               |2={{Clade
                  |1={{Clade
                     |1=[[w:Evanioidea|Evanioidea]]
                     |2=[[w:Stephanoidea|Stephanoidea]]
                     }}
                  |2={{Clade
                     |1=[[w:Trigonaloidea|Trigonaloidea]]
                     |label2=[[w:Aculeata|Aculeata]]
                     |2={{Clade
                        |1=[[w:Chrysidoidea|Chrysidoidea]]
                        |2={{Clade
                           |1=[[w:Vespoidea|Vespoidea]] (potter, honey and social wasps)
                           |2={{Clade
                              |1={{Clade
                                 |1=[[w:Pompiloidea|Pompiloidea]] (velvet ants, spider wasps and relatives)
                                 |2={{Clade
                                    |1=[[w:Thynnoidea|Thynnoidea]]
                                    |2=[[w:Tiphioidea|Tiphioidea]]
                                 }} }}
                              |2={{Clade
                                 |1=[[w:Scolioidea|Scolioidea]]
                                 |2={{Clade
                                    |1=[[w:Formicoidea|Formicoidea]] (ants)
                                    |2=[[w:Apoidea|Apoidea]] (bees and related wasps)
}} }} }} }} }} }} }} }} }}
&lt;br&gt;

==Some common African Symphyta==
&lt;gallery mode=packed heights=200&gt;
Sawfly, Argidae 2021 12 19 12 39 42.jpg|Sawfly, ''Arge'' sp. (Argidae, Superfamily Tenthredinoidea) 
Athalia 2019 11 21 0815.jpg|Sawfly, ''Athalia'' sp. (Tenthredinidae, Superfamily Tenthredinoidea) 
Athalia 2019 08 23 8964.jpg|Sawfly, ''Athalia'' sp. (Tenthredinidae, Superfamily Tenthredinoidea) 
Sirex noctilio F (prof.).JPG|''Sirex noctilio'', a pest in ''Pinus'' plantations (introduced to Africa)&lt;ref name=WaspWebSn&gt;[https://www.waspweb.org/Siricoidea/Siricidae/Sirex/Sirex_noctilio.htm van Noort, Simon (2023). WaspWeb: ''Sirex noctilio''. www.waspweb.org/Classification/index.htm Retrieved 22 February 2023.]&lt;/ref&gt;
&lt;/gallery&gt;

== Frequently reported African Apocrita ==
&lt;br&gt;
[[w:Aculeata|Aculeata]] (ants, bees and stinging wasps) are the most commonly observed Hymenoptera in Africa. There are many more photographs of African Aculeata on the web - See [https://www.waspweb.org/Classification/index.htm African Aculeata on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=326777 African Aculeata on iNaturalist] &lt;br&gt;
&lt;gallery mode=packed heights=200&gt;
Slender Ant (Tetraponera natalensis) (30538051244).jpg|Slender ant (Formicidae, Formicoidea)
Carpenter Bee (Xylocopa inconstans, female) (6021534858).jpg|Female carpenter bee (Apidae, Apoidea)
Chalybion 2019 12 02 2314.jpg|Blue mud-dauber wasp (Sphecidae, Apoidea)
Bethylidae 2019 08 21 13 42 21 8760.jpg|Flat wasp (Bethylidae, Chrysidoidea)
Belonogaster juncea colonialis, manlik, h, Pretoria.jpg|Paper wasp (Vespidae, Vespoidea)
Meria 2020 08 12 2193.jpg|''Meria'' sp. female (Thynnidae, Thynnoidea)
Dasylabris stimulatrix iNat37068107 2019 12 23 2990 W.jpg|''Dasylabris stimulatrix'', a velvet ant (Mutillidae, Pompiloidea)
Pompilidae 2019 05 28 0247.jpg|Spider-hunting wasp (Pompilidae, Pompiloidea)
Scoliid Wasp 2019 06 08 0492.jpg|Campsomerine wasp (Scoliidae, Scolioidea)
&lt;/gallery&gt;&lt;br&gt;

Darwin wasps ([[w:Ichneumonidae|Ichneumonidae]]) and braconids ([[w:Braconidae|Braconidae]]) are also frequently reported. Links to [https://www.waspweb.org/Ichneumonoidea/index.htm African Ichneumonoidea on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=47200 African Ichneumonoidea on iNaturalist].&lt;br&gt;
&lt;gallery mode=packed heights=200&gt;
Echthromorpha agrestoria 2019 10 03 5572.jpg|''Echthromorpha agrestoria'' (Ichneumonidae, Ichneumonoidea)
Ichneumonidae inat 88832241.jpg|''Goryphus tricolor'' (Ichneumonidae, Ichneumonoidea)
Braconid Wasp (Archibracon servillei) (11857083186).jpg|Braconine wasp (Braconidae, Ichneumonoidea) 
2019 09 15 12 55 07 Microgastrinae 38425632.jpg|Microgastrine wasp (Braconidae, Ichneumonoidea) 
&lt;/gallery&gt;&lt;br&gt;

Small [[w:Chalcidoidea|chalcidoid]] parasitic wasps (especially those from the families [[w:Pteromalidae|Pteromalidae]], [[w:Chalcididae|Chalcididae]], [[w:Eulophidae|Eulophidae]], [[w:Eurytomidae|Eurytomidae]]) are also common. Links to [https://www.waspweb.org/Chalcidoidea/index.htm African Chalcidoidea on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=69750 African Chalcidoidea on iNaturalist]
&lt;gallery mode=packed heights=200&gt;
Halticoptera 2019 11 26 2173Cedara.jpg|''Halticoptera'' sp. (Pteromalidae, Chalcidoidea)
Brachymeria 2019 10 09 17 26 38 2520.jpg|''Brachymeria'' sp. (Chalcididae, Chalcidoidea)
Eulophidae Inat 38422095 b.jpg|''Hemiptarsenus'' sp. (Eulophidae, Chalcidoidea)
Eurytomidae00.jpg|Mating seed chalcids (Eurytomidae, Chalcidoidea)
&lt;/gallery&gt;

==References==
{{reflist}}</text>
      <sha1>1xbkj2kj4r4c3ruh7kamkc3nj522me6</sha1>
    </revision>
    <revision>
      <id>2815795</id>
      <parentid>2815791</parentid>
      <timestamp>2026-06-15T11:49:57Z</timestamp>
      <contributor>
        <username>Alandmanson</username>
        <id>1669821</id>
      </contributor>
      <comment>/* Subfamily Bembicinae */</comment>
      <origin>2815795</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16736" sha1="neyx779fhv5ang3bhvnjb8i1czcghm0" xml:space="preserve">= Superfamily Apoidea =
== African Ampulicidae ==
&lt;gallery mode=packed heights=150&gt;
Ampulicidae 37894270 suncana.jpg|''Ampulex apicalis''
Dolichurus cf basuto iN 99066897 Sep 29, 2021.jpg|''Dolichurus'' cf ''basuto''
&lt;/gallery&gt;

== African Astatidae ==
&lt;gallery mode=packed heights=150&gt;
Astata iN 105162782 Nicola van Berkel.jpg|''Astata'' sp.
Astata melanaria.jpg|''Astata melanaria''
&lt;/gallery&gt;

== African Bembicidae ==
===Subfamily Bembicinae===	
&lt;gallery mode=packed heights=150&gt;
Bembecinus iN 153052948.jpg|''Bembecinus'' sp.
Bembix iN 195581985.jpg|''Bembix'' sp.
Bembix capensis 386097016.jpg|''Bembix capensis''
Gorytes natalensis 112517046.jpg|''Gorytes natalensis''
Hoplisoides thalia iN 268375748 a.jpg|''Hoplisoides thalia''
Sand wasp (Stizus fuscipennis).jpg|''Stizus fuscipennis''
Stizus imperialis.jpg|''Stizus imperialis''
&lt;/gallery&gt;		
Tribe Gorytini	
*		''Afrogorytes''
*		''Gorytes''
*		''Harpactus''
*		''Hoplisoides''
*		''Lestiphorus''
		
Tribe Spheciini	
*		''Ammatomus''
*		''Kohlia''
*		''Sphecius''
		
Tribe Handlirschiini	
*		''Handlirschia''
		
Tribe Bembicini	
*		''Bembix''
		
Tribe Stizini	
*		''Bembecinus''
*		''Stizoides''
*		''Stizus''

===Subfamily Nyssoninae===	
*		''Brachystegus''
*		''Hovanysson''
*		''Nysson''
		
===Subfamily Alyssontinae===	
*		''Alysson''
*		''Didineis''

== African Crabronidae ==
&lt;gallery mode=packed heights=150&gt;
Dasyproctus iN 30029277 a.jpg
Dicranorhina kohli 2023 07 25 iN 176115975.jpg
Liris on Crassula iN 42678436 01.jpg
Oxybelus iN 250449990 2024 10 09 - 02.jpg
Palarus Bee Pirate iN 144133368 2022-12-01 01.jpg
Paranysson iN 199673489 1.jpg
Pison iN 144131685 2022-11-30 03.jpg
Tachysphex iN 250449986 2024 10 09 7305.jpg
Tachytes iN 188902572 1964.jpg
Trypoxylon iN 99063113 a.jpg
&lt;/gallery&gt;

== African Pemphredonidae ==
&lt;gallery mode=packed heights=150&gt;
Polemistus braunsii iNaturalist 228280708.jpg

&lt;/gallery&gt;

== African Philanthidae ==
&lt;gallery mode=packed heights=150&gt;
Philanthus triangulum diadema 187037342.jpg
Cerceris 2019 12 02 2310.jpg
&lt;/gallery&gt;

== African Psenidae ==
&lt;gallery mode=packed heights=150&gt;
Psenini iN 1022563 i c riddell.jpg

&lt;/gallery&gt;

== African Sphecidae ==
&lt;gallery mode=packed heights=150&gt;
Chalybion 2019 12 02 2314.jpg
Thread-waisted Sand Wasp (Ammophila sp.) carrying a Lienard's Achaea (Achaea lienardi) caterpillar ... (52715218455).jpg
Ammophila ferrugineipes04.jpg
Black Mud-dauber Wasp (Sceliphron spirifex) on Buffalo-Thorn (Ziziphus mucronata) flowers ... (52739846889).jpg
&lt;/gallery&gt;

= Superfamily Chalcidoidea =
 
Chalcidoidea is an incredibly diverse group of wasps with a wide variety of life histories; many are parasitoids, making them ecologically important; some are used for biological control of insect pests. About 22 000 species have been described, but as many as 500 000 are thought to exist worldwide.&lt;ref name=Noyes2019/&gt;

Most chalcidoids are small (body length less than 5 mm), the smallest being males of the mymarid ''Dicopomorpha echmepterygis'', which is the smallest known flying insect (0.13 mm).&lt;ref name=Noyes2019&gt;Noyes, J.S. 2019. Universal Chalcidoidea Database. [http://www.nhm.ac.uk/chalcidoids]&lt;/ref&gt; However, some species may be as long as 20 mm (excluding antennae and ovipositor), such as the pelecinellid ''Doddifoenus wallacei''.&lt;ref name=Krogmann&amp;Burks2009&gt;Krogmann, Lars; Burks, Roger A. (2009-12-31). &quot;Doddifoenus wallacei, a new giant parasitoid wasp of the subfamily Leptofoeninae (Chalcidoidea: Pteromalidae), with a description of its mesosomal skeletal anatomy and a molecular characterization&quot;. Zootaxa. 2194: 21–36. doi:10.5281/zenodo.189452 [https://www.researchgate.net/profile/Lars-Krogmann/publication/250916337 PDF]&lt;/ref&gt; Many have bright metallic colours, hence the name Chalcidoidea or chalcid - the greek word χαλκός (chalcos) means copper or bronze.&lt;ref name=Perseus2023&gt;[http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0073:entry=xalko/s Georg Autenrieth, A Homeric Dictionary]&lt;/ref&gt;

Many new chalcidoid families were proposed in 2022.&lt;ref name=Burks2022&gt;Burks, R., Mitroiu, M.D., Fusu, L., Heraty, J.M., Janšta, P., Heydon, S., Papilloud, N.D.S., Peters, R.S., Tselikh, E.V., Woolley, J.B. and van Noort, S., (2022).﻿ From hell’s heart I stab at thee! A determined approach towards a monophyletic Pteromalidae and reclassification of Chalcidoidea (Hymenoptera). Journal of Hymenoptera Research, 94, pp.13-88. [https://doi.org/10.3897/jhr.94.94263 DOI]&lt;/ref&gt; This was largely based on phylogenetic evidence (both molecular and morphological) accumulated since the families of the Superfamily were outlined in 1993&lt;ref name=Gibson1993&gt;Gibson, G.A.P. (1993) Superfamilies Mymarommatoidea and Chalcidoidea (pp. 570-655). In Goulet, H. &amp; Huber, J. (eds). Hymenoptera of the World: an identification guide to families. Research Branch, Agriculture Canada, Ottawa, Canada, 668 pp. [https://www.researchgate.net/publication/259227143 PDF]&lt;/ref&gt;.


Burks, R., Mitroiu, M.D., Fusu, L., Heraty, J.M., Janšta, P., Heydon, S., Papilloud, N.D.S., Peters, R.S., Tselikh, E.V., Woolley, J.B. and van Noort, S., (2022).﻿ From hell’s heart I stab at thee! A determined approach towards a monophyletic Pteromalidae and reclassification of Chalcidoidea (Hymenoptera). Journal of Hymenoptera Research, 94, pp.13-88. https://doi.org/10.3897/jhr.94.94263

Cruaud, A., Rasplus, J.Y., Zhang, J., Burks, R., Delvare, G., Fusu, L., Gumovsky, A., Huber, J.T., Janšta, P., Mitroiu, M.D. and Noyes, J.S., 2022. The Chalcidoidea bush of life–a massive radiation blurred by mutational saturation. bioRxiv. https://doi.org/10.1101/2022.09.11.507458 https://www.biorxiv.org/content/10.1101/2022.09.11.507458.full.pdf


= Superfamily Ichneumonoidea =

Quicke, D.L., 2015. The braconid and ichneumonid parasitoid wasps: biology, systematics, evolution and ecology. John Wiley &amp; Sons.
https://www.researchgate.net/publication/281662102_The_Braconid_and_Ichneumonid_Parasitoid_Wasps_Biology_Systematics_Evolution_and_Ecology

=== Diplazontinae ===
Quote from Fitton &amp; Rotheray (1982):
&quot;Diplazontines are distinguished easily from other ichneumonids by their general appearance (Fig. 1). The main confirmatory characters are the bifid upper tooth of the mandible (Fig. 2) and the sub-rectangular shape of the first tergite of the gaster (Figs. 1,3,4, 13, 15 and 17). In fact, the diplazontines are so distinct that they can be separated from all other Hymenoptera-Apocrita by possession of the following five characters in combination: (1) antenna of seventeen or more segments (Fig. I); (2) forewing with costal cell obliterated (that is, veins C and Sc + R + Rs contiguous from the wing base to the base of the pterostigma (Fig. 6 ) ; (3) forewing with cross-vein 2 mcu present (Fig. 6); (4) mandible with its upper tooth subdivided (bifid), making the mandible tridentate (Fig. 2); (5) first tergite of gaster sub-rectangular in shape (that is, subequal in width anteriorly and posteriorly) (Figs. 1 , 3 , 4 , 13,15 and 17).&quot;

Fitton, M. G., &amp; Rotheray, G. E. (1982). A key to the European genera of diplazontine ichneumon‐flies, with notes on the British fauna. Systematic Entomology, 7(3), 311-320.

=== Superfamily Pompiloidea ===
Family Mutillidae (Velvet ants)
Family Pompilidae (Spider hunting wasps)
Family Sapygidae (Sapygid wasps)


== Spider-hunting wasps ==
Two wasps from the genus ''Auplopus'' from Europe. Most of the ''Auplopus'' species, along with others from the Tribe Ageniellini, amputate the legs of the spiders they capture; this makes it much easier to move the spider to the nest.
&lt;gallery mode=packed heights=200&gt;
Auplopus carbonarius IMG 1624.jpg
Auplopus carbonarius fg01 20060623 Nied Garten.jpg
&lt;/gallery&gt;
African genera of Ageniellini:
* ''[[Auplopus]]'' &lt;small&gt;Spinola, 1841&lt;/small&gt;
* ''[[Cyemagenia]]'' &lt;small&gt;Arnold, 1946&lt;/small&gt;
* ''[[Dichragenia]]'' &lt;small&gt;Haupt, 1950&lt;/small&gt;
* ''[[Phanagenia]]'' &lt;small&gt;Banks, 1933&lt;/small&gt;   Madagascar
* ''[[Poecilagenia]]'' &lt;small&gt;Haupt, 1926&lt;/small&gt;

== Superfamily Scolioidea ==
=== Family Bradynobaenidae (Bradynobaenid wasps) ===
=== Family Scoliidae (Mammoth wasps) ===

== Superfamily Tiphioidea ==
Family Tiphiidae (Tiphiid wasps)
== Superfamily Thynnoidea ==
Family Thynnidae(Thynnid wasps)
== Superfamily Vespoidea ==
=== Family Rhopalosomatidae (Rhopalosomatid wasps) ===
===Family Vespidae (Paper, Potter &amp; Pollen wasps)===


== '''&lt;big&gt;Hymenoptera&lt;/big&gt;''' ==
About 20 000 described species of [[w:Hymenoptera|Hymenoptera]] (wasps, bees, ants and sawflies) are known from the [[w:Afrotropical|Afrotropical]] region. Estimates of the actual species count for the region range from 100 000 species to as high as 500 000 species.&lt;ref name=WaspWebOverview&gt;[https://www.waspweb.org/Afrotropical_Hymenoptera_book/Background_and_Motivation.htm van Noort, Simon (2023). WaspWeb: Afrotropical Hymenoptera Initiative. www.waspweb.org/Afrotropical_Hymenoptera_book/Background_and_Motivation.htm Retrieved 22 February 2023.]&lt;/ref&gt; Nineteen different superfamilies are illustrated on [[User:Alandmanson/Hymenoptera of southern Africa|this gallery]] in Wikimedia Commons.

The huge number of undescribed species means that many species will be extinct before we are even aware of them, as there are too few taxonomists employed to tackle the task of describing all of them in the next few decades.

==Classification==
The Order can be split into two Suborders - The [[w:Symphyta|Symphyta]] (Woodwasps, Horntails, Sawflies) and the [[w:Apocrita|Apocrita]] (Narrow-waisted wasps, ants and bees).&lt;br&gt;

When compared to the temperate regions of the northern hemisphere, the diversity of Symphyta in Africa is relatively poor, although sawflies of the Superfamily [[w:Tenthredinoidea|Tenthredinoidea]] are fairly common in forests and other woody vegetation types.

Africa has a rich diversity of Apocrita. The cladogram shown below&lt;ref name=Peters&gt;{{Cite journal |last1=Peters |first1=Ralph S. |last2=Krogmann |first2=Lars |last3=Mayer |first3=Christoph |last4=Donath |first4=Alexander |last5=Gunkel |first5=Simon |last6=Meusemann |first6=Karen |last7=Kozlov |first7=Alexey |last8=Podsiadlowski |first8=Lars |last9=Petersen |first9=Malte |title=Evolutionary History of the Hymenoptera |journal=Current Biology |volume=27 |issue=7 |pages=1013–1018 |doi=10.1016/j.cub.2017.01.027|pmid=28343967 |year=2017 |doi-access=free }}&lt;/ref&gt; indicates the possible relationships between 11 of the superfamilies that comprise Apocrita; These 11 superfamilies are all represented in Africa. This breakdown is used by iNaturalist.&lt;ref name=inat-Aculeata&gt;https://www.inaturalist.org/taxa/326777-Aculeata&lt;/ref&gt; It is, however, not accepted by all hymenopterists, and may change as more phylogenetic evidence is accumulated.&lt;ref name=waspwebClass&gt;[https://www.waspweb.org/Classification/index.htm van Noort, Simon (2023). WaspWeb: Classification of Afrotropical Hymenoptera (Wasps, Bees, Ants). www.waspweb.org/Classification/index.htm Retrieved 22 February 2023.]&lt;/ref&gt;
{{Clade|style=font-size:85%; line-height:85%
|label1=Apocrita
            |1={{Clade
               |label1=[[w:Parasitoida|Parasitoida]]
               |1={{Clade
                  |1={{Clade
                     |1=[[w:Ceraphronoidea|Ceraphronoidea]]
                     |2=[[w:Ichneumonoidea|Ichneumonoidea]]
                     }}
                  |label2=[[w:Proctotrupomorpha|Proctotrupomorpha]]
                  |2={{Clade
                     |1=[[w:Cynipoidea|Cynipoidea]]
                     |2={{Clade
                        |1=[[w:Platygastroidea|Platygastroidea]]
                        |2={{Clade
                           |1=[[w:Chalcidoidea|Chalcidoidea]]
                           |2={{Clade
                              |1=[[w:Diaprioidea|Diaprioidea]]
                              |2=[[w:Proctotrupoidea|Proctotrupoidea]]
                  }} }} }} }} }}
               |2={{Clade
                  |1={{Clade
                     |1=[[w:Evanioidea|Evanioidea]]
                     |2=[[w:Stephanoidea|Stephanoidea]]
                     }}
                  |2={{Clade
                     |1=[[w:Trigonaloidea|Trigonaloidea]]
                     |label2=[[w:Aculeata|Aculeata]]
                     |2={{Clade
                        |1=[[w:Chrysidoidea|Chrysidoidea]]
                        |2={{Clade
                           |1=[[w:Vespoidea|Vespoidea]] (potter, honey and social wasps)
                           |2={{Clade
                              |1={{Clade
                                 |1=[[w:Pompiloidea|Pompiloidea]] (velvet ants, spider wasps and relatives)
                                 |2={{Clade
                                    |1=[[w:Thynnoidea|Thynnoidea]]
                                    |2=[[w:Tiphioidea|Tiphioidea]]
                                 }} }}
                              |2={{Clade
                                 |1=[[w:Scolioidea|Scolioidea]]
                                 |2={{Clade
                                    |1=[[w:Formicoidea|Formicoidea]] (ants)
                                    |2=[[w:Apoidea|Apoidea]] (bees and related wasps)
}} }} }} }} }} }} }} }} }}
&lt;br&gt;

==Some common African Symphyta==
&lt;gallery mode=packed heights=200&gt;
Sawfly, Argidae 2021 12 19 12 39 42.jpg|Sawfly, ''Arge'' sp. (Argidae, Superfamily Tenthredinoidea) 
Athalia 2019 11 21 0815.jpg|Sawfly, ''Athalia'' sp. (Tenthredinidae, Superfamily Tenthredinoidea) 
Athalia 2019 08 23 8964.jpg|Sawfly, ''Athalia'' sp. (Tenthredinidae, Superfamily Tenthredinoidea) 
Sirex noctilio F (prof.).JPG|''Sirex noctilio'', a pest in ''Pinus'' plantations (introduced to Africa)&lt;ref name=WaspWebSn&gt;[https://www.waspweb.org/Siricoidea/Siricidae/Sirex/Sirex_noctilio.htm van Noort, Simon (2023). WaspWeb: ''Sirex noctilio''. www.waspweb.org/Classification/index.htm Retrieved 22 February 2023.]&lt;/ref&gt;
&lt;/gallery&gt;

== Frequently reported African Apocrita ==
&lt;br&gt;
[[w:Aculeata|Aculeata]] (ants, bees and stinging wasps) are the most commonly observed Hymenoptera in Africa. There are many more photographs of African Aculeata on the web - See [https://www.waspweb.org/Classification/index.htm African Aculeata on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=326777 African Aculeata on iNaturalist] &lt;br&gt;
&lt;gallery mode=packed heights=200&gt;
Slender Ant (Tetraponera natalensis) (30538051244).jpg|Slender ant (Formicidae, Formicoidea)
Carpenter Bee (Xylocopa inconstans, female) (6021534858).jpg|Female carpenter bee (Apidae, Apoidea)
Chalybion 2019 12 02 2314.jpg|Blue mud-dauber wasp (Sphecidae, Apoidea)
Bethylidae 2019 08 21 13 42 21 8760.jpg|Flat wasp (Bethylidae, Chrysidoidea)
Belonogaster juncea colonialis, manlik, h, Pretoria.jpg|Paper wasp (Vespidae, Vespoidea)
Meria 2020 08 12 2193.jpg|''Meria'' sp. female (Thynnidae, Thynnoidea)
Dasylabris stimulatrix iNat37068107 2019 12 23 2990 W.jpg|''Dasylabris stimulatrix'', a velvet ant (Mutillidae, Pompiloidea)
Pompilidae 2019 05 28 0247.jpg|Spider-hunting wasp (Pompilidae, Pompiloidea)
Scoliid Wasp 2019 06 08 0492.jpg|Campsomerine wasp (Scoliidae, Scolioidea)
&lt;/gallery&gt;&lt;br&gt;

Darwin wasps ([[w:Ichneumonidae|Ichneumonidae]]) and braconids ([[w:Braconidae|Braconidae]]) are also frequently reported. Links to [https://www.waspweb.org/Ichneumonoidea/index.htm African Ichneumonoidea on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=47200 African Ichneumonoidea on iNaturalist].&lt;br&gt;
&lt;gallery mode=packed heights=200&gt;
Echthromorpha agrestoria 2019 10 03 5572.jpg|''Echthromorpha agrestoria'' (Ichneumonidae, Ichneumonoidea)
Ichneumonidae inat 88832241.jpg|''Goryphus tricolor'' (Ichneumonidae, Ichneumonoidea)
Braconid Wasp (Archibracon servillei) (11857083186).jpg|Braconine wasp (Braconidae, Ichneumonoidea) 
2019 09 15 12 55 07 Microgastrinae 38425632.jpg|Microgastrine wasp (Braconidae, Ichneumonoidea) 
&lt;/gallery&gt;&lt;br&gt;

Small [[w:Chalcidoidea|chalcidoid]] parasitic wasps (especially those from the families [[w:Pteromalidae|Pteromalidae]], [[w:Chalcididae|Chalcididae]], [[w:Eulophidae|Eulophidae]], [[w:Eurytomidae|Eurytomidae]]) are also common. Links to [https://www.waspweb.org/Chalcidoidea/index.htm African Chalcidoidea on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=69750 African Chalcidoidea on iNaturalist]
&lt;gallery mode=packed heights=200&gt;
Halticoptera 2019 11 26 2173Cedara.jpg|''Halticoptera'' sp. (Pteromalidae, Chalcidoidea)
Brachymeria 2019 10 09 17 26 38 2520.jpg|''Brachymeria'' sp. (Chalcididae, Chalcidoidea)
Eulophidae Inat 38422095 b.jpg|''Hemiptarsenus'' sp. (Eulophidae, Chalcidoidea)
Eurytomidae00.jpg|Mating seed chalcids (Eurytomidae, Chalcidoidea)
&lt;/gallery&gt;

==References==
{{reflist}}</text>
      <sha1>neyx779fhv5ang3bhvnjb8i1czcghm0</sha1>
    </revision>
    <revision>
      <id>2815796</id>
      <parentid>2815795</parentid>
      <timestamp>2026-06-15T11:57:01Z</timestamp>
      <contributor>
        <username>Alandmanson</username>
        <id>1669821</id>
      </contributor>
      <comment>/* Subfamily Bembicinae */</comment>
      <origin>2815796</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16786" sha1="cfhfo7x652k5shx3jrc0iqglctn1jxe" xml:space="preserve">= Superfamily Apoidea =
== African Ampulicidae ==
&lt;gallery mode=packed heights=150&gt;
Ampulicidae 37894270 suncana.jpg|''Ampulex apicalis''
Dolichurus cf basuto iN 99066897 Sep 29, 2021.jpg|''Dolichurus'' cf ''basuto''
&lt;/gallery&gt;

== African Astatidae ==
&lt;gallery mode=packed heights=150&gt;
Astata iN 105162782 Nicola van Berkel.jpg|''Astata'' sp.
Astata melanaria.jpg|''Astata melanaria''
&lt;/gallery&gt;

== African Bembicidae ==
===Subfamily Bembicinae===	
&lt;gallery mode=packed heights=150&gt;
Bembecinus iN 153052948.jpg|''Bembecinus'' sp.
Bembix iN 195581985.jpg|''Bembix'' sp.
Bembix capensis 386097016.jpg|''Bembix capensis''
Bembix triangulifera.png|''Bembix triangulifera''
Gorytes natalensis 112517046.jpg|''Gorytes natalensis''
Hoplisoides thalia iN 268375748 a.jpg|''Hoplisoides thalia''
Sand wasp (Stizus fuscipennis).jpg|''Stizus fuscipennis''
Stizus imperialis.jpg|''Stizus imperialis''
&lt;/gallery&gt;		
Tribe Gorytini	
*		''Afrogorytes''
*		''Gorytes''
*		''Harpactus''
*		''Hoplisoides''
*		''Lestiphorus''
		
Tribe Spheciini	
*		''Ammatomus''
*		''Kohlia''
*		''Sphecius''
		
Tribe Handlirschiini	
*		''Handlirschia''
		
Tribe Bembicini	
*		''Bembix''
		
Tribe Stizini	
*		''Bembecinus''
*		''Stizoides''
*		''Stizus''

===Subfamily Nyssoninae===	
*		''Brachystegus''
*		''Hovanysson''
*		''Nysson''
		
===Subfamily Alyssontinae===	
*		''Alysson''
*		''Didineis''

== African Crabronidae ==
&lt;gallery mode=packed heights=150&gt;
Dasyproctus iN 30029277 a.jpg
Dicranorhina kohli 2023 07 25 iN 176115975.jpg
Liris on Crassula iN 42678436 01.jpg
Oxybelus iN 250449990 2024 10 09 - 02.jpg
Palarus Bee Pirate iN 144133368 2022-12-01 01.jpg
Paranysson iN 199673489 1.jpg
Pison iN 144131685 2022-11-30 03.jpg
Tachysphex iN 250449986 2024 10 09 7305.jpg
Tachytes iN 188902572 1964.jpg
Trypoxylon iN 99063113 a.jpg
&lt;/gallery&gt;

== African Pemphredonidae ==
&lt;gallery mode=packed heights=150&gt;
Polemistus braunsii iNaturalist 228280708.jpg

&lt;/gallery&gt;

== African Philanthidae ==
&lt;gallery mode=packed heights=150&gt;
Philanthus triangulum diadema 187037342.jpg
Cerceris 2019 12 02 2310.jpg
&lt;/gallery&gt;

== African Psenidae ==
&lt;gallery mode=packed heights=150&gt;
Psenini iN 1022563 i c riddell.jpg

&lt;/gallery&gt;

== African Sphecidae ==
&lt;gallery mode=packed heights=150&gt;
Chalybion 2019 12 02 2314.jpg
Thread-waisted Sand Wasp (Ammophila sp.) carrying a Lienard's Achaea (Achaea lienardi) caterpillar ... (52715218455).jpg
Ammophila ferrugineipes04.jpg
Black Mud-dauber Wasp (Sceliphron spirifex) on Buffalo-Thorn (Ziziphus mucronata) flowers ... (52739846889).jpg
&lt;/gallery&gt;

= Superfamily Chalcidoidea =
 
Chalcidoidea is an incredibly diverse group of wasps with a wide variety of life histories; many are parasitoids, making them ecologically important; some are used for biological control of insect pests. About 22 000 species have been described, but as many as 500 000 are thought to exist worldwide.&lt;ref name=Noyes2019/&gt;

Most chalcidoids are small (body length less than 5 mm), the smallest being males of the mymarid ''Dicopomorpha echmepterygis'', which is the smallest known flying insect (0.13 mm).&lt;ref name=Noyes2019&gt;Noyes, J.S. 2019. Universal Chalcidoidea Database. [http://www.nhm.ac.uk/chalcidoids]&lt;/ref&gt; However, some species may be as long as 20 mm (excluding antennae and ovipositor), such as the pelecinellid ''Doddifoenus wallacei''.&lt;ref name=Krogmann&amp;Burks2009&gt;Krogmann, Lars; Burks, Roger A. (2009-12-31). &quot;Doddifoenus wallacei, a new giant parasitoid wasp of the subfamily Leptofoeninae (Chalcidoidea: Pteromalidae), with a description of its mesosomal skeletal anatomy and a molecular characterization&quot;. Zootaxa. 2194: 21–36. doi:10.5281/zenodo.189452 [https://www.researchgate.net/profile/Lars-Krogmann/publication/250916337 PDF]&lt;/ref&gt; Many have bright metallic colours, hence the name Chalcidoidea or chalcid - the greek word χαλκός (chalcos) means copper or bronze.&lt;ref name=Perseus2023&gt;[http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0073:entry=xalko/s Georg Autenrieth, A Homeric Dictionary]&lt;/ref&gt;

Many new chalcidoid families were proposed in 2022.&lt;ref name=Burks2022&gt;Burks, R., Mitroiu, M.D., Fusu, L., Heraty, J.M., Janšta, P., Heydon, S., Papilloud, N.D.S., Peters, R.S., Tselikh, E.V., Woolley, J.B. and van Noort, S., (2022).﻿ From hell’s heart I stab at thee! A determined approach towards a monophyletic Pteromalidae and reclassification of Chalcidoidea (Hymenoptera). Journal of Hymenoptera Research, 94, pp.13-88. [https://doi.org/10.3897/jhr.94.94263 DOI]&lt;/ref&gt; This was largely based on phylogenetic evidence (both molecular and morphological) accumulated since the families of the Superfamily were outlined in 1993&lt;ref name=Gibson1993&gt;Gibson, G.A.P. (1993) Superfamilies Mymarommatoidea and Chalcidoidea (pp. 570-655). In Goulet, H. &amp; Huber, J. (eds). Hymenoptera of the World: an identification guide to families. Research Branch, Agriculture Canada, Ottawa, Canada, 668 pp. [https://www.researchgate.net/publication/259227143 PDF]&lt;/ref&gt;.


Burks, R., Mitroiu, M.D., Fusu, L., Heraty, J.M., Janšta, P., Heydon, S., Papilloud, N.D.S., Peters, R.S., Tselikh, E.V., Woolley, J.B. and van Noort, S., (2022).﻿ From hell’s heart I stab at thee! A determined approach towards a monophyletic Pteromalidae and reclassification of Chalcidoidea (Hymenoptera). Journal of Hymenoptera Research, 94, pp.13-88. https://doi.org/10.3897/jhr.94.94263

Cruaud, A., Rasplus, J.Y., Zhang, J., Burks, R., Delvare, G., Fusu, L., Gumovsky, A., Huber, J.T., Janšta, P., Mitroiu, M.D. and Noyes, J.S., 2022. The Chalcidoidea bush of life–a massive radiation blurred by mutational saturation. bioRxiv. https://doi.org/10.1101/2022.09.11.507458 https://www.biorxiv.org/content/10.1101/2022.09.11.507458.full.pdf


= Superfamily Ichneumonoidea =

Quicke, D.L., 2015. The braconid and ichneumonid parasitoid wasps: biology, systematics, evolution and ecology. John Wiley &amp; Sons.
https://www.researchgate.net/publication/281662102_The_Braconid_and_Ichneumonid_Parasitoid_Wasps_Biology_Systematics_Evolution_and_Ecology

=== Diplazontinae ===
Quote from Fitton &amp; Rotheray (1982):
&quot;Diplazontines are distinguished easily from other ichneumonids by their general appearance (Fig. 1). The main confirmatory characters are the bifid upper tooth of the mandible (Fig. 2) and the sub-rectangular shape of the first tergite of the gaster (Figs. 1,3,4, 13, 15 and 17). In fact, the diplazontines are so distinct that they can be separated from all other Hymenoptera-Apocrita by possession of the following five characters in combination: (1) antenna of seventeen or more segments (Fig. I); (2) forewing with costal cell obliterated (that is, veins C and Sc + R + Rs contiguous from the wing base to the base of the pterostigma (Fig. 6 ) ; (3) forewing with cross-vein 2 mcu present (Fig. 6); (4) mandible with its upper tooth subdivided (bifid), making the mandible tridentate (Fig. 2); (5) first tergite of gaster sub-rectangular in shape (that is, subequal in width anteriorly and posteriorly) (Figs. 1 , 3 , 4 , 13,15 and 17).&quot;

Fitton, M. G., &amp; Rotheray, G. E. (1982). A key to the European genera of diplazontine ichneumon‐flies, with notes on the British fauna. Systematic Entomology, 7(3), 311-320.

=== Superfamily Pompiloidea ===
Family Mutillidae (Velvet ants)
Family Pompilidae (Spider hunting wasps)
Family Sapygidae (Sapygid wasps)


== Spider-hunting wasps ==
Two wasps from the genus ''Auplopus'' from Europe. Most of the ''Auplopus'' species, along with others from the Tribe Ageniellini, amputate the legs of the spiders they capture; this makes it much easier to move the spider to the nest.
&lt;gallery mode=packed heights=200&gt;
Auplopus carbonarius IMG 1624.jpg
Auplopus carbonarius fg01 20060623 Nied Garten.jpg
&lt;/gallery&gt;
African genera of Ageniellini:
* ''[[Auplopus]]'' &lt;small&gt;Spinola, 1841&lt;/small&gt;
* ''[[Cyemagenia]]'' &lt;small&gt;Arnold, 1946&lt;/small&gt;
* ''[[Dichragenia]]'' &lt;small&gt;Haupt, 1950&lt;/small&gt;
* ''[[Phanagenia]]'' &lt;small&gt;Banks, 1933&lt;/small&gt;   Madagascar
* ''[[Poecilagenia]]'' &lt;small&gt;Haupt, 1926&lt;/small&gt;

== Superfamily Scolioidea ==
=== Family Bradynobaenidae (Bradynobaenid wasps) ===
=== Family Scoliidae (Mammoth wasps) ===

== Superfamily Tiphioidea ==
Family Tiphiidae (Tiphiid wasps)
== Superfamily Thynnoidea ==
Family Thynnidae(Thynnid wasps)
== Superfamily Vespoidea ==
=== Family Rhopalosomatidae (Rhopalosomatid wasps) ===
===Family Vespidae (Paper, Potter &amp; Pollen wasps)===


== '''&lt;big&gt;Hymenoptera&lt;/big&gt;''' ==
About 20 000 described species of [[w:Hymenoptera|Hymenoptera]] (wasps, bees, ants and sawflies) are known from the [[w:Afrotropical|Afrotropical]] region. Estimates of the actual species count for the region range from 100 000 species to as high as 500 000 species.&lt;ref name=WaspWebOverview&gt;[https://www.waspweb.org/Afrotropical_Hymenoptera_book/Background_and_Motivation.htm van Noort, Simon (2023). WaspWeb: Afrotropical Hymenoptera Initiative. www.waspweb.org/Afrotropical_Hymenoptera_book/Background_and_Motivation.htm Retrieved 22 February 2023.]&lt;/ref&gt; Nineteen different superfamilies are illustrated on [[User:Alandmanson/Hymenoptera of southern Africa|this gallery]] in Wikimedia Commons.

The huge number of undescribed species means that many species will be extinct before we are even aware of them, as there are too few taxonomists employed to tackle the task of describing all of them in the next few decades.

==Classification==
The Order can be split into two Suborders - The [[w:Symphyta|Symphyta]] (Woodwasps, Horntails, Sawflies) and the [[w:Apocrita|Apocrita]] (Narrow-waisted wasps, ants and bees).&lt;br&gt;

When compared to the temperate regions of the northern hemisphere, the diversity of Symphyta in Africa is relatively poor, although sawflies of the Superfamily [[w:Tenthredinoidea|Tenthredinoidea]] are fairly common in forests and other woody vegetation types.

Africa has a rich diversity of Apocrita. The cladogram shown below&lt;ref name=Peters&gt;{{Cite journal |last1=Peters |first1=Ralph S. |last2=Krogmann |first2=Lars |last3=Mayer |first3=Christoph |last4=Donath |first4=Alexander |last5=Gunkel |first5=Simon |last6=Meusemann |first6=Karen |last7=Kozlov |first7=Alexey |last8=Podsiadlowski |first8=Lars |last9=Petersen |first9=Malte |title=Evolutionary History of the Hymenoptera |journal=Current Biology |volume=27 |issue=7 |pages=1013–1018 |doi=10.1016/j.cub.2017.01.027|pmid=28343967 |year=2017 |doi-access=free }}&lt;/ref&gt; indicates the possible relationships between 11 of the superfamilies that comprise Apocrita; These 11 superfamilies are all represented in Africa. This breakdown is used by iNaturalist.&lt;ref name=inat-Aculeata&gt;https://www.inaturalist.org/taxa/326777-Aculeata&lt;/ref&gt; It is, however, not accepted by all hymenopterists, and may change as more phylogenetic evidence is accumulated.&lt;ref name=waspwebClass&gt;[https://www.waspweb.org/Classification/index.htm van Noort, Simon (2023). WaspWeb: Classification of Afrotropical Hymenoptera (Wasps, Bees, Ants). www.waspweb.org/Classification/index.htm Retrieved 22 February 2023.]&lt;/ref&gt;
{{Clade|style=font-size:85%; line-height:85%
|label1=Apocrita
            |1={{Clade
               |label1=[[w:Parasitoida|Parasitoida]]
               |1={{Clade
                  |1={{Clade
                     |1=[[w:Ceraphronoidea|Ceraphronoidea]]
                     |2=[[w:Ichneumonoidea|Ichneumonoidea]]
                     }}
                  |label2=[[w:Proctotrupomorpha|Proctotrupomorpha]]
                  |2={{Clade
                     |1=[[w:Cynipoidea|Cynipoidea]]
                     |2={{Clade
                        |1=[[w:Platygastroidea|Platygastroidea]]
                        |2={{Clade
                           |1=[[w:Chalcidoidea|Chalcidoidea]]
                           |2={{Clade
                              |1=[[w:Diaprioidea|Diaprioidea]]
                              |2=[[w:Proctotrupoidea|Proctotrupoidea]]
                  }} }} }} }} }}
               |2={{Clade
                  |1={{Clade
                     |1=[[w:Evanioidea|Evanioidea]]
                     |2=[[w:Stephanoidea|Stephanoidea]]
                     }}
                  |2={{Clade
                     |1=[[w:Trigonaloidea|Trigonaloidea]]
                     |label2=[[w:Aculeata|Aculeata]]
                     |2={{Clade
                        |1=[[w:Chrysidoidea|Chrysidoidea]]
                        |2={{Clade
                           |1=[[w:Vespoidea|Vespoidea]] (potter, honey and social wasps)
                           |2={{Clade
                              |1={{Clade
                                 |1=[[w:Pompiloidea|Pompiloidea]] (velvet ants, spider wasps and relatives)
                                 |2={{Clade
                                    |1=[[w:Thynnoidea|Thynnoidea]]
                                    |2=[[w:Tiphioidea|Tiphioidea]]
                                 }} }}
                              |2={{Clade
                                 |1=[[w:Scolioidea|Scolioidea]]
                                 |2={{Clade
                                    |1=[[w:Formicoidea|Formicoidea]] (ants)
                                    |2=[[w:Apoidea|Apoidea]] (bees and related wasps)
}} }} }} }} }} }} }} }} }}
&lt;br&gt;

==Some common African Symphyta==
&lt;gallery mode=packed heights=200&gt;
Sawfly, Argidae 2021 12 19 12 39 42.jpg|Sawfly, ''Arge'' sp. (Argidae, Superfamily Tenthredinoidea) 
Athalia 2019 11 21 0815.jpg|Sawfly, ''Athalia'' sp. (Tenthredinidae, Superfamily Tenthredinoidea) 
Athalia 2019 08 23 8964.jpg|Sawfly, ''Athalia'' sp. (Tenthredinidae, Superfamily Tenthredinoidea) 
Sirex noctilio F (prof.).JPG|''Sirex noctilio'', a pest in ''Pinus'' plantations (introduced to Africa)&lt;ref name=WaspWebSn&gt;[https://www.waspweb.org/Siricoidea/Siricidae/Sirex/Sirex_noctilio.htm van Noort, Simon (2023). WaspWeb: ''Sirex noctilio''. www.waspweb.org/Classification/index.htm Retrieved 22 February 2023.]&lt;/ref&gt;
&lt;/gallery&gt;

== Frequently reported African Apocrita ==
&lt;br&gt;
[[w:Aculeata|Aculeata]] (ants, bees and stinging wasps) are the most commonly observed Hymenoptera in Africa. There are many more photographs of African Aculeata on the web - See [https://www.waspweb.org/Classification/index.htm African Aculeata on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=326777 African Aculeata on iNaturalist] &lt;br&gt;
&lt;gallery mode=packed heights=200&gt;
Slender Ant (Tetraponera natalensis) (30538051244).jpg|Slender ant (Formicidae, Formicoidea)
Carpenter Bee (Xylocopa inconstans, female) (6021534858).jpg|Female carpenter bee (Apidae, Apoidea)
Chalybion 2019 12 02 2314.jpg|Blue mud-dauber wasp (Sphecidae, Apoidea)
Bethylidae 2019 08 21 13 42 21 8760.jpg|Flat wasp (Bethylidae, Chrysidoidea)
Belonogaster juncea colonialis, manlik, h, Pretoria.jpg|Paper wasp (Vespidae, Vespoidea)
Meria 2020 08 12 2193.jpg|''Meria'' sp. female (Thynnidae, Thynnoidea)
Dasylabris stimulatrix iNat37068107 2019 12 23 2990 W.jpg|''Dasylabris stimulatrix'', a velvet ant (Mutillidae, Pompiloidea)
Pompilidae 2019 05 28 0247.jpg|Spider-hunting wasp (Pompilidae, Pompiloidea)
Scoliid Wasp 2019 06 08 0492.jpg|Campsomerine wasp (Scoliidae, Scolioidea)
&lt;/gallery&gt;&lt;br&gt;

Darwin wasps ([[w:Ichneumonidae|Ichneumonidae]]) and braconids ([[w:Braconidae|Braconidae]]) are also frequently reported. Links to [https://www.waspweb.org/Ichneumonoidea/index.htm African Ichneumonoidea on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=47200 African Ichneumonoidea on iNaturalist].&lt;br&gt;
&lt;gallery mode=packed heights=200&gt;
Echthromorpha agrestoria 2019 10 03 5572.jpg|''Echthromorpha agrestoria'' (Ichneumonidae, Ichneumonoidea)
Ichneumonidae inat 88832241.jpg|''Goryphus tricolor'' (Ichneumonidae, Ichneumonoidea)
Braconid Wasp (Archibracon servillei) (11857083186).jpg|Braconine wasp (Braconidae, Ichneumonoidea) 
2019 09 15 12 55 07 Microgastrinae 38425632.jpg|Microgastrine wasp (Braconidae, Ichneumonoidea) 
&lt;/gallery&gt;&lt;br&gt;

Small [[w:Chalcidoidea|chalcidoid]] parasitic wasps (especially those from the families [[w:Pteromalidae|Pteromalidae]], [[w:Chalcididae|Chalcididae]], [[w:Eulophidae|Eulophidae]], [[w:Eurytomidae|Eurytomidae]]) are also common. Links to [https://www.waspweb.org/Chalcidoidea/index.htm African Chalcidoidea on WaspWeb] and [https://www.inaturalist.org/observations?place_id=97392&amp;taxon_id=69750 African Chalcidoidea on iNaturalist]
&lt;gallery mode=packed heights=200&gt;
Halticoptera 2019 11 26 2173Cedara.jpg|''Halticoptera'' sp. (Pteromalidae, Chalcidoidea)
Brachymeria 2019 10 09 17 26 38 2520.jpg|''Brachymeria'' sp. (Chalcididae, Chalcidoidea)
Eulophidae Inat 38422095 b.jpg|''Hemiptarsenus'' sp. (Eulophidae, Chalcidoidea)
Eurytomidae00.jpg|Mating seed chalcids (Eurytomidae, Chalcidoidea)
&lt;/gallery&gt;

==References==
{{reflist}}</text>
      <sha1>cfhfo7x652k5shx3jrc0iqglctn1jxe</sha1>
    </revision>
  </page>
  <page>
    <title>Bully Metric Timestamps</title>
    <ns>0</ns>
    <id>305659</id>
    <revision>
      <id>2815717</id>
      <parentid>2814559</parentid>
      <timestamp>2026-06-15T01:37:16Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The Metonic Cycle */</comment>
      <origin>2815717</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="20521" sha1="cg2k1k5gshtm9d6sfu3ioy29fdsxhh1" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>cg2k1k5gshtm9d6sfu3ioy29fdsxhh1</sha1>
    </revision>
    <revision>
      <id>2815718</id>
      <parentid>2815717</parentid>
      <timestamp>2026-06-15T01:37:31Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815718</origin>
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      <text bytes="20524" sha1="c1p4qi9y9tcxybwktph220p3aw64awu" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>c1p4qi9y9tcxybwktph220p3aw64awu</sha1>
    </revision>
    <revision>
      <id>2815719</id>
      <parentid>2815718</parentid>
      <timestamp>2026-06-15T01:39:16Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815719</origin>
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      <text bytes="19732" sha1="osi4moh6nhh8z9m5cj5h1uv2xyr299a" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>osi4moh6nhh8z9m5cj5h1uv2xyr299a</sha1>
    </revision>
    <revision>
      <id>2815720</id>
      <parentid>2815719</parentid>
      <timestamp>2026-06-15T01:41:14Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815720</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19741" sha1="5i2oxuovsb0lijjryp8at7ck2r7dtis" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 13}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>5i2oxuovsb0lijjryp8at7ck2r7dtis</sha1>
    </revision>
    <revision>
      <id>2815721</id>
      <parentid>2815720</parentid>
      <timestamp>2026-06-15T01:43:00Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815721</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19748" sha1="bso3h4rlt9g9tpcbrgr0mtz1x01od8m" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1st Quarter}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 13}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>bso3h4rlt9g9tpcbrgr0mtz1x01od8m</sha1>
    </revision>
    <revision>
      <id>2815722</id>
      <parentid>2815721</parentid>
      <timestamp>2026-06-15T01:44:21Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815722</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19769" sha1="0zfqgdnmqrb94m9ahzs02b4amqvcc9j" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 13}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>0zfqgdnmqrb94m9ahzs02b4amqvcc9j</sha1>
    </revision>
    <revision>
      <id>2815723</id>
      <parentid>2815722</parentid>
      <timestamp>2026-06-15T01:45:03Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
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      <text bytes="19748" sha1="sjuqeefnlabtor1a4yz2250ba297bme" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 13}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>sjuqeefnlabtor1a4yz2250ba297bme</sha1>
    </revision>
    <revision>
      <id>2815724</id>
      <parentid>2815723</parentid>
      <timestamp>2026-06-15T01:45:21Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815724</origin>
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      <text bytes="19748" sha1="fombq8drgbrf434yt7gi206lwcyf4x6" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: The Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 13}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>fombq8drgbrf434yt7gi206lwcyf4x6</sha1>
    </revision>
    <revision>
      <id>2815725</id>
      <parentid>2815724</parentid>
      <timestamp>2026-06-15T01:45:56Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815725</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19667" sha1="6mvzsyd9xkrs4nijs3w0w3m1cyaf8a1" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: The Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 13}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>6mvzsyd9xkrs4nijs3w0w3m1cyaf8a1</sha1>
    </revision>
    <revision>
      <id>2815726</id>
      <parentid>2815725</parentid>
      <timestamp>2026-06-15T01:46:33Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815726</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19591" sha1="7ro011whzbydoomv7ulveiknxhzs00m" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: The Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 13}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>7ro011whzbydoomv7ulveiknxhzs00m</sha1>
    </revision>
    <revision>
      <id>2815727</id>
      <parentid>2815726</parentid>
      <timestamp>2026-06-15T01:47:09Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815727</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19595" sha1="2p2xnyl368ogzs7mlrtkkkkzqg9y7dt" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: The Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One Galactic Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 13}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>2p2xnyl368ogzs7mlrtkkkkzqg9y7dt</sha1>
    </revision>
    <revision>
      <id>2815728</id>
      <parentid>2815727</parentid>
      <timestamp>2026-06-15T01:56:30Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815728</origin>
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      <format>text/x-wiki</format>
      <text bytes="19594" sha1="9ovn3qpb71tipx5ojxcsin2i9le9okd" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: The Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One Galactic Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>9ovn3qpb71tipx5ojxcsin2i9le9okd</sha1>
    </revision>
    <revision>
      <id>2815729</id>
      <parentid>2815728</parentid>
      <timestamp>2026-06-15T01:57:26Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
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      <text bytes="19606" sha1="p3hnqtejldog25lbk0yafsq3jkj552q" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: A &lt;br /&gt; Galactic &lt;br /&gt; Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One Galactic Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>p3hnqtejldog25lbk0yafsq3jkj552q</sha1>
    </revision>
    <revision>
      <id>2815730</id>
      <parentid>2815729</parentid>
      <timestamp>2026-06-15T01:58:02Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815730</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19606" sha1="bdrzkq0qo9o3sjwv1jz73s3zn6kiwt5" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | A &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>bdrzkq0qo9o3sjwv1jz73s3zn6kiwt5</sha1>
    </revision>
    <revision>
      <id>2815731</id>
      <parentid>2815730</parentid>
      <timestamp>2026-06-15T02:00:36Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815731</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19606" sha1="7n5z337okmsq6zgsr1sddl7zkokyfuh" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | A &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>7n5z337okmsq6zgsr1sddl7zkokyfuh</sha1>
    </revision>
    <revision>
      <id>2815732</id>
      <parentid>2815731</parentid>
      <timestamp>2026-06-15T02:01:12Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815732</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19608" sha1="7is9knso66nb31i3s4g30z5g8tire5g" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>7is9knso66nb31i3s4g30z5g8tire5g</sha1>
    </revision>
    <revision>
      <id>2815733</id>
      <parentid>2815732</parentid>
      <timestamp>2026-06-15T02:01:50Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
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      <comment>/* Galactic Years and Weeks */</comment>
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      <text bytes="19609" sha1="18hm4r7hzkht2kikmhapaphu3ybe44m" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 3: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>18hm4r7hzkht2kikmhapaphu3ybe44m</sha1>
    </revision>
    <revision>
      <id>2815734</id>
      <parentid>2815733</parentid>
      <timestamp>2026-06-15T02:06:58Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
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      <text bytes="19714" sha1="3zmj14mzytnd1z76bmd8ndjv7rnmdu3" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 3: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>3zmj14mzytnd1z76bmd8ndjv7rnmdu3</sha1>
    </revision>
    <revision>
      <id>2815735</id>
      <parentid>2815734</parentid>
      <timestamp>2026-06-15T02:08:33Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815735</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19714" sha1="k47nls0afouglmela5n5i520ychc3um" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>k47nls0afouglmela5n5i520ychc3um</sha1>
    </revision>
    <revision>
      <id>2815736</id>
      <parentid>2815735</parentid>
      <timestamp>2026-06-15T02:11:30Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815736</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="17182" sha1="ey3skqq3rgubgo9mprx10mymprkgt5y" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}

|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
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      <id>2815737</id>
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        <username>Unitfreak</username>
        <id>695864</id>
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      <text bytes="17690" sha1="5hr7g2sa16f8g2b1zl2b37t029qn71o" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|821D 89D8 9D8B}} || {{nowrap|829D 89D8 9D8B}} || {{nowrap|831D 89D8 9D8B}} || {{nowrap|839D 89D8 9D8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8227 6276 2764}} || {{nowrap|82A7 6276 2764}} || {{nowrap|8327 6276 2764}} || {{nowrap|83A7 6276 2764}}


|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
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    <revision>
      <id>2815738</id>
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      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
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      <text bytes="17688" sha1="14kwlbx1tein8gdin7vvaruxny3yw0y" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D8B}} || {{nowrap|829D 89D8 9D8B}} || {{nowrap|831D 89D8 9D8B}} || {{nowrap|839D 89D8 9D8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2764}} || {{nowrap|82A7 6276 2764}} || {{nowrap|8327 6276 2764}} || {{nowrap|83A7 6276 2764}}

|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>14kwlbx1tein8gdin7vvaruxny3yw0y</sha1>
    </revision>
    <revision>
      <id>2815739</id>
      <parentid>2815738</parentid>
      <timestamp>2026-06-15T02:19:26Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815739</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="17944" sha1="8vt8xdwgp7atxvuqyxb22f618gy7tg5" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D8B}} || {{nowrap|829D 89D8 9D8B}} || {{nowrap|831D 89D8 9D8B}} || {{nowrap|839D 89D8 9D8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2764}} || {{nowrap|82A7 6276 2764}} || {{nowrap|8327 6276 2764}} || {{nowrap|83A7 6276 2764}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13D}} || {{nowrap|82B1 3B13 B13D}} || {{nowrap|8331 3B13 B13D}} || {{nowrap|83B1 3B13 B13D}}


|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>8vt8xdwgp7atxvuqyxb22f618gy7tg5</sha1>
    </revision>
    <revision>
      <id>2815741</id>
      <parentid>2815739</parentid>
      <timestamp>2026-06-15T02:21:44Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815741</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="18194" sha1="0z9xk3wep54awy2sjnhfzkq8patrt4y" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D8B}} || {{nowrap|829D 89D8 9D8B}} || {{nowrap|831D 89D8 9D8B}} || {{nowrap|839D 89D8 9D8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2764}} || {{nowrap|82A7 6276 2764}} || {{nowrap|8327 6276 2764}} || {{nowrap|83A7 6276 2764}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13D}} || {{nowrap|82B1 3B13 B13D}} || {{nowrap|8331 3B13 B13D}} || {{nowrap|83B1 3B13 B13D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|823B 13B1 3B16}} || {{nowrap|82BB 13B1 3B16}} || {{nowrap|833B 13B1 3B16}} || {{nowrap|83BB 13B1 3B16}}

|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
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      <text bytes="18194" sha1="pcyabauuqxkkzlxq8wmtgz11xpywiqt" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D8B}} || {{nowrap|829D 89D8 9D8B}} || {{nowrap|831D 89D8 9D8B}} || {{nowrap|839D 89D8 9D8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2764}} || {{nowrap|82A7 6276 2764}} || {{nowrap|8327 6276 2764}} || {{nowrap|83A7 6276 2764}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13D}} || {{nowrap|82B1 3B13 B13D}} || {{nowrap|8331 3B13 B13D}} || {{nowrap|83B1 3B13 B13D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B16}} || {{nowrap|82BB 13B1 3B16}} || {{nowrap|833B 13B1 3B16}} || {{nowrap|83BB 13B1 3B16}}

|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
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      <text bytes="18449" sha1="6k0pecdyhsyceu5yt71xhd663teisz1" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D8B}} || {{nowrap|829D 89D8 9D8B}} || {{nowrap|831D 89D8 9D8B}} || {{nowrap|839D 89D8 9D8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2764}} || {{nowrap|82A7 6276 2764}} || {{nowrap|8327 6276 2764}} || {{nowrap|83A7 6276 2764}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13D}} || {{nowrap|82B1 3B13 B13D}} || {{nowrap|8331 3B13 B13D}} || {{nowrap|83B1 3B13 B13D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B16}} || {{nowrap|82BB 13B1 3B16}} || {{nowrap|833B 13B1 3B16}} || {{nowrap|83BB 13B1 3B16}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EF}} || {{nowrap|82C4 EC4E C4EF}} || {{nowrap|8344 EC4E C4EF}} || {{nowrap|83C4 EC4E C4EF}}


|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>6k0pecdyhsyceu5yt71xhd663teisz1</sha1>
    </revision>
    <revision>
      <id>2815750</id>
      <parentid>2815745</parentid>
      <timestamp>2026-06-15T02:34:19Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815750</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="18449" sha1="0x81b2s7bz3whgvc9sfuf11vzngiw1h" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2764}} || {{nowrap|82A7 6276 2764}} || {{nowrap|8327 6276 2764}} || {{nowrap|83A7 6276 2764}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13D}} || {{nowrap|82B1 3B13 B13D}} || {{nowrap|8331 3B13 B13D}} || {{nowrap|83B1 3B13 B13D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B16}} || {{nowrap|82BB 13B1 3B16}} || {{nowrap|833B 13B1 3B16}} || {{nowrap|83BB 13B1 3B16}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EF}} || {{nowrap|82C4 EC4E C4EF}} || {{nowrap|8344 EC4E C4EF}} || {{nowrap|83C4 EC4E C4EF}}


|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
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    <revision>
      <id>2815751</id>
      <parentid>2815750</parentid>
      <timestamp>2026-06-15T02:35:15Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
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      <text bytes="18449" sha1="46r3sjlgd30um71xwibtkb71v4mt1ep" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13D}} || {{nowrap|82B1 3B13 B13D}} || {{nowrap|8331 3B13 B13D}} || {{nowrap|83B1 3B13 B13D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B16}} || {{nowrap|82BB 13B1 3B16}} || {{nowrap|833B 13B1 3B16}} || {{nowrap|83BB 13B1 3B16}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EF}} || {{nowrap|82C4 EC4E C4EF}} || {{nowrap|8344 EC4E C4EF}} || {{nowrap|83C4 EC4E C4EF}}


|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
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    <revision>
      <id>2815752</id>
      <parentid>2815751</parentid>
      <timestamp>2026-06-15T02:36:28Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
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      <text bytes="18449" sha1="nlj7cz1h3emkqkzl5qpmnsq0xws1hcg" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B16}} || {{nowrap|82BB 13B1 3B16}} || {{nowrap|833B 13B1 3B16}} || {{nowrap|83BB 13B1 3B16}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EF}} || {{nowrap|82C4 EC4E C4EF}} || {{nowrap|8344 EC4E C4EF}} || {{nowrap|83C4 EC4E C4EF}}


|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>nlj7cz1h3emkqkzl5qpmnsq0xws1hcg</sha1>
    </revision>
    <revision>
      <id>2815753</id>
      <parentid>2815752</parentid>
      <timestamp>2026-06-15T02:39:16Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
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      <text bytes="18447" sha1="iemqsitcaen9v9b0lon43b6blryqifk" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}

|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>iemqsitcaen9v9b0lon43b6blryqifk</sha1>
    </revision>
    <revision>
      <id>2815754</id>
      <parentid>2815753</parentid>
      <timestamp>2026-06-15T02:42:21Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815754</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="18701" sha1="b9o7oyba7darpecg4hk89zacffv320h" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}

|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}

|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>b9o7oyba7darpecg4hk89zacffv320h</sha1>
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      <id>2815756</id>
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      <timestamp>2026-06-15T02:44:57Z</timestamp>
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        <username>Unitfreak</username>
        <id>695864</id>
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      <comment>/* Galactic Years and Weeks */</comment>
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      <text bytes="18955" sha1="f555zm5dciwtjlgbtz6pfg0woitqi2o" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}


|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
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      <text bytes="19206" sha1="3q83ryop2qok34f8n9lic7o66czjmud" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}

|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>3q83ryop2qok34f8n9lic7o66czjmud</sha1>
    </revision>
    <revision>
      <id>2815761</id>
      <parentid>2815759</parentid>
      <timestamp>2026-06-15T02:51:56Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815761</origin>
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      <format>text/x-wiki</format>
      <text bytes="19460" sha1="1oecxiztbrl40g502e3tl6i1rrs26s5" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}

|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>1oecxiztbrl40g502e3tl6i1rrs26s5</sha1>
    </revision>
    <revision>
      <id>2815762</id>
      <parentid>2815761</parentid>
      <timestamp>2026-06-15T02:54:07Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815762</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19714" sha1="dfilqfetptho53g9y4ijwul7ak0wppe" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>dfilqfetptho53g9y4ijwul7ak0wppe</sha1>
    </revision>
    <revision>
      <id>2815763</id>
      <parentid>2815762</parentid>
      <timestamp>2026-06-15T02:56:59Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815763</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19863" sha1="pbyg798s6miplsm669eje51y09k1lcp" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
The galactic year, also known as a cosmic year, is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>pbyg798s6miplsm669eje51y09k1lcp</sha1>
    </revision>
    <revision>
      <id>2815765</id>
      <parentid>2815763</parentid>
      <timestamp>2026-06-15T03:04:30Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815765</origin>
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      <text bytes="20060" sha1="8n5xhapnjqpz22q9e0b4xhll5e4hojl" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
The '''galactic year''', also known as a '''cosmic year''', is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. A '''Galactic Week''' can be defined as the approximate duration of time required for the Sun to orbit '''6.9 degrees''', so that 52 galactic weeks is equivalent to one galactic year.
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>8n5xhapnjqpz22q9e0b4xhll5e4hojl</sha1>
    </revision>
    <revision>
      <id>2815766</id>
      <parentid>2815765</parentid>
      <timestamp>2026-06-15T03:05:01Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Realized vs. Estimated Bully timestamps */</comment>
      <origin>2815766</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19358" sha1="2rgt0p387vgmuufcqw1d1yli08y7ahf" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Galactic Years and Weeks ====
The '''galactic year''', also known as a '''cosmic year''', is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. A '''Galactic Week''' can be defined as the approximate duration of time required for the Sun to orbit '''6.9 degrees''', so that 52 galactic weeks is equivalent to one galactic year.
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>2rgt0p387vgmuufcqw1d1yli08y7ahf</sha1>
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    <revision>
      <id>2815767</id>
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      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
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      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815767</origin>
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      <text bytes="19361" sha1="r4giftfs22b8pz5ccv2i0awtu58q1wc" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Galactic Years and Weeks ====
The '''galactic year''', also known as a '''cosmic year''', is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. A '''galactic week''' can be thought of as the approximate duration of time required for the Sun to orbit '''6.9 degrees''', so that 52 galactic weeks is equivalent to one galactic year.
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | One &lt;br /&gt; Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>r4giftfs22b8pz5ccv2i0awtu58q1wc</sha1>
    </revision>
    <revision>
      <id>2815768</id>
      <parentid>2815767</parentid>
      <timestamp>2026-06-15T03:07:35Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815768</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19350" sha1="64ydovtfd9h1lauye001zik9z85bb4u" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Galactic Years and Weeks ====
The '''galactic year''', also known as a '''cosmic year''', is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. A '''galactic week''' can be thought of as the approximate duration of time required for the Sun to orbit '''6.9 degrees''', so that 52 galactic weeks is equivalent to one galactic year.
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>64ydovtfd9h1lauye001zik9z85bb4u</sha1>
    </revision>
    <revision>
      <id>2815770</id>
      <parentid>2815768</parentid>
      <timestamp>2026-06-15T03:08:32Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815770</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="19352" sha1="2hjf36jx79rq0ttditzy3bi3zf2r7ho" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Galactic Years and Weeks ====
The '''galactic year''', also known as a '''cosmic year''', is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. A '''galactic week''' can be thought of as the duration of time required for the Sun to orbit approximately '''6.9 degrees''', so that 52 galactic weeks is equivalent to one galactic year.
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
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    </revision>
    <revision>
      <id>2815772</id>
      <parentid>2815770</parentid>
      <timestamp>2026-06-15T03:24:28Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Relativistic and Cosmological Considerations */</comment>
      <origin>2815772</origin>
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      <text bytes="20054" sha1="nx4qno9tjk84k6ezw2l1fh743q9hkzf" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Galactic Years and Weeks ====
The '''galactic year''', also known as a '''cosmic year''', is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. A '''galactic week''' can be thought of as the duration of time required for the Sun to orbit approximately '''6.9 degrees''', so that 52 galactic weeks is equivalent to one galactic year.
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>nx4qno9tjk84k6ezw2l1fh743q9hkzf</sha1>
    </revision>
    <revision>
      <id>2815773</id>
      <parentid>2815772</parentid>
      <timestamp>2026-06-15T03:25:24Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Realized vs. Estimated Bully timestamps */</comment>
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      <text bytes="19352" sha1="2hjf36jx79rq0ttditzy3bi3zf2r7ho" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Galactic Years and Weeks ====
The '''galactic year''', also known as a '''cosmic year''', is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. A '''galactic week''' can be thought of as the duration of time required for the Sun to orbit approximately '''6.9 degrees''', so that 52 galactic weeks is equivalent to one galactic year.
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>2hjf36jx79rq0ttditzy3bi3zf2r7ho</sha1>
    </revision>
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      <text bytes="20054" sha1="d4ro9e6ve9dw0rmnxj8alqwfudxeavj" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
The '''galactic year''', also known as a '''cosmic year''', is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. A '''galactic week''' can be thought of as the duration of time required for the Sun to orbit approximately '''6.9 degrees''', so that 52 galactic weeks is equivalent to one galactic year.
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>d4ro9e6ve9dw0rmnxj8alqwfudxeavj</sha1>
    </revision>
    <revision>
      <id>2815776</id>
      <parentid>2815774</parentid>
      <timestamp>2026-06-15T03:26:24Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Relativistic and Cosmological Considerations */</comment>
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      <text bytes="17823" sha1="qzauqbcxew2rxmoy8ms67p5jf39sht3" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

==== Galactic Years and Weeks ====
The '''galactic year''', also known as a '''cosmic year''', is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. A '''galactic week''' can be thought of as the duration of time required for the Sun to orbit approximately '''6.9 degrees''', so that 52 galactic weeks is equivalent to one galactic year.
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
      <sha1>qzauqbcxew2rxmoy8ms67p5jf39sht3</sha1>
    </revision>
    <revision>
      <id>2815777</id>
      <parentid>2815776</parentid>
      <timestamp>2026-06-15T03:26:47Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* Galactic Years and Weeks */</comment>
      <origin>2815777</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="20054" sha1="dt8sj01p5rtl7hq1jj1zpvip6tc5szq" xml:space="preserve">&lt;small&gt;[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt; &lt;/small&gt;

In the '''Bully Timestamp System''', time is measured using 12-digit [[w:hexadecimal|hexadecimal]] &quot;Bully timestamps,&quot; with a new timestamp realized every 3,055 SI seconds (TAI). With 12 hexadecimal digits, the system has a enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is:

:&lt;math&gt;16^{12} \times 3,055 \text{ seconds} \approx 27.25 \text{ billion years}&lt;/math&gt;

[[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]]

== Bully timestamp Divisions ==
The Bully system's time range is divided into three distinct sets:

=== First Set ===
* ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Measures time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* First timestamp: ''{{mono|0000 0000 0000}}''
** [[w:Cosmic_inflation|Cosmic Inflation]]
** [[w:Baryogenesis|Baryogenesis]]
** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]]
* Approximately: ''{{mono|0000 EA00 0000}}''
** [[w:Decoupling_(cosmology)|Decoupling]]
** [[w:Recombination_(cosmology)|Recombination]]
* Approximately: ''{{mono|0100 0000 0000}}''
** [[w:Star_formation|First Star Formation]]
* Approximately: ''{{mono|0297 0000 0000}}''
** [[w:MoM-z14|Oldest Observed Galaxy]]
&lt;/div&gt;

=== Second Set ===
* ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'': Tracks cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
* Approximately: ''{{mono|3B00 0000 0000}}''
** [[w:Murchison_meteorite|Oldest Presolar Grains]]
* Approximately: ''{{mono|5720 9000 0000}}''
** [[w:Hadean|Hadean Eon Begins]]
* Approximately: ''{{mono|5C2A 0000 0000}}''
** [[w:Archean|Archean Eon Begins]]
* Approximately: ''{{mono|6A8C 0000 0000}}''
** [[w:Proterozoic|Proterozoic Eon Begins]]
* Approximately: ''{{mono|7D56 0000 0000}}''
** [[w:Phanerozoic|Phanerozoic Eon Begins]]
&lt;/div&gt;

[[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]]
 (Ma) represents one million (10&lt;sup&gt;6&lt;/sup&gt;) years.]]

=== Third Set ===
* ''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years.

==== Realized vs. Estimated Bully timestamps ====
Each Bully timestamp is realized exactly 3055 seconds TAI after the previous one.  However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an estimate of how elapsed time might have transpired in the past, rather than an actual realization of Bully time. Bully time should only be considered &quot;realized&quot; when time is measured with an accuracy of &lt;math&gt;{10}^{-10}&lt;/math&gt;. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present).

[[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]]

=== Relativistic and Cosmological Considerations ===
What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference?

The &quot;age of the universe&quot; cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the &quot;CMB rest frame.&quot;

Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 2800 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All &quot;realized&quot; Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference.

Furthermore, the &quot;estimated&quot; Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 2800 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited.

[[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]]

==== Galactic Years and Weeks ====
The '''galactic year''', also known as a '''cosmic year''', is the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. A '''galactic week''' can be thought of as the duration of time required for the Sun to orbit approximately '''6.9 degrees''', so that 52 galactic weeks is equivalent to one galactic year.
[[File:Motion_of_Sun,_Earth_and_Moon_around_the_Milky_Way.jpg|frame|center|text-bottom|thumb|Figure 3:]]

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Figure 4: One Galactic Year

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! style=&quot;padding: 10px; font-size: large;&quot; | Galactic &lt;br /&gt; Year
|| {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 0}} || {{nowrap|8200 0000 0000}} || {{nowrap|8280 0000 0000}} || {{nowrap|8300 0000 0000}} || {{nowrap|8380 0000 0000}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 1}} || {{nowrap|8209 D89D 89D8}} || {{nowrap|8289 D89D 89D8}} || {{nowrap|8309 D89D 89D8}} || {{nowrap|8389 D89D 89D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 2}} || {{nowrap|8213 B13B 13B1}} || {{nowrap|8293 B13B 13B1}} || {{nowrap|8313 B13B 13B1}} || {{nowrap|8393 B13B 13B1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 3}} || {{nowrap|821D 89D8 9D89}} || {{nowrap|829D 89D8 9D89}} || {{nowrap|831D 89D8 9D89}} || {{nowrap|839D 89D8 9D89}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 4}} || {{nowrap|8227 6276 2762}} || {{nowrap|82A7 6276 2762}} || {{nowrap|8327 6276 2762}} || {{nowrap|83A7 6276 2762}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 5}} || {{nowrap|8231 3B13 B13B}} || {{nowrap|82B1 3B13 B13B}} || {{nowrap|8331 3B13 B13B}} || {{nowrap|83B1 3B13 B13B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 6}} || {{nowrap|823B 13B1 3B13}} || {{nowrap|82BB 13B1 3B13}} || {{nowrap|833B 13B1 3B13}} || {{nowrap|83BB 13B1 3B13}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 7}} || {{nowrap|8244 EC4E C4EC}} || {{nowrap|82C4 EC4E C4EC}} || {{nowrap|8344 EC4E C4EC}} || {{nowrap|83C4 EC4E C4EC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 8}} || {{nowrap|824E C4EC 4EC4}} || {{nowrap|82CE C4EC 4EC4}} || {{nowrap|834E C4EC 4EC4}} || {{nowrap|83CE C4EC 4EC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 9}} || {{nowrap|8258 9D89 D89D}} || {{nowrap|82D8 9D89 D89D}} || {{nowrap|8358 9D89 D89D}} || {{nowrap|83D8 9D89 D89D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 10}} || {{nowrap|8262 7627 6276}} || {{nowrap|82E2 7627 6276}} || {{nowrap|8362 7627 6276}} || {{nowrap|83E2 7627 6276}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 11}} || {{nowrap|826C 4EC4 EC4E}} || {{nowrap|82EC 4EC4 EC4E}} || {{nowrap|836C 4EC4 EC4E}} || {{nowrap|83EC 4EC4 EC4E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Week 12}} || {{nowrap|8276 2762 7627}} || {{nowrap|82F6 2762 7627}} || {{nowrap|8376 2762 7627}} || {{nowrap|83F6 2762 7627}}
|}

==== The Metonic Cycle ====
The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list:
&lt;div style=&quot;background-color: #f0f4f7; padding: 15px; border-left: 5px solid #009688;&quot;&gt;
July 23 New Moon Metonic Cycles
* July 23, 1998 on 8209 280'''0 038B'''
* July 23, 2017 on 8209 280'''3 0238'''
* July 23, 2036 on 8209 280'''6 00EA'''
* July 23, 2055 on 8209 280'''8 FF9B'''
* July 23, 2074 on 8209 280'''B FE45'''
* July 23, 2093 on 8209 280'''E FCE6'''
&lt;/div&gt;


[[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]]

== Contextualized vs. Decontextualized Time ==

Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is &quot;contextual&quot; because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic &quot;leaps&quot; (seconds and years). In '''Figure 3''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1.

In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to &quot;true time&quot; at any specific geographical location. Represented by the black lines in '''Figure 3''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures.

[[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 3: Modern Time Keeping]]

The various decontextualized standards currently in use are effectively &quot;frozen&quot; in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds.

The Bully timestamp system, shown on the far-right axis of '''Figure 3''', follows the same uniform, decontextualized logic as TAI and TT but avoids this &quot;legacy offset&quot; confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret.

[[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]]

== Why do we need Bully timestamps? ==

All the timestamps in '''Figure 4''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. 

{| class=&quot;wikitable&quot; style=&quot;margin-right: 0; margin-left: 1em; text-align: center;&quot;
|+ Figure 4: UTC Time Zones vs. Bully Timestamps.
|-
! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps]
|-
| rowspan = 3 |
[[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0|
June 21, 1998 at  8:59:29 pm (JST)&lt;/br&gt;
June 21, 1998 at  7:59:29 pm (CST)&lt;/br&gt;
June 21, 1998 at  2:59:29 pm (EEST)&lt;/br&gt;
June 21, 1998 at 12:59:29 pm (IST)&lt;/br&gt;
June 21, 1998 at 11:59:29 am (GMT)&lt;/br&gt;
June 21, 1998 at  8:59:29 am (BRT)&lt;/br&gt;
June 21, 1998 at  4:59:29 am (PDT)&lt;/br&gt;
June 21, 1998 at  1:59:29 am (HST)&lt;/br&gt;
]]
||
[[File:WorldMap-Blank-Noborders.svg|thumb|&lt;br/&gt;
06/21/1998 12:00:32.184 (TT)&lt;br/&gt;
06/21/1998 12:00:00 (TAI)&lt;br/&gt;
06/21/1998 11:59:42 (GPS)
]]
|-
! Bully Timestamp
|-
||
[[File:WorldMap-Blank-Noborders.svg|thumb|8209 2800 0000 (+ 0.000 sec)]]
|}

==== Legacy Decontextualized Timestamps ====

The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 4''' attempt to solve the UTC geographic fragmentation problem, yet they remain &quot;cluttered&quot; by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several &quot;leap&quot; seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time.

For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains &quot;tethered&quot; to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome &quot;hybrids&quot; that attempt to measure linear time using units designed for Earth’s rotation.

==== Decontextualized Bully Timestamps ====

The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 4''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 2800 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time.

Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format:

[http://www.leapsecond.com/m/gps.htm LeapSecond.com]

[https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com]

[http://www.csgnetwork.com/multitimedisp.html csgnetwork.com]

== The Foundations of Bully Metric ==

The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to &lt;math&gt;10,330 \times 3,055&lt;/math&gt; SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system.

The name &quot;Bully&quot; is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, &quot;bully&quot; means '''&quot;beautiful&quot; or &quot;excellent,&quot;''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of &quot;bullies&quot; like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system.

* [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]]
* [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]]

== The Bully Mnemonic ==

&lt;math display=&quot;block&quot;&gt; {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; {1 \, Tropical \, Year} = {31,556,926 \, Seconds} &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt; 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years &lt;/math&gt;

&lt;math display=&quot;block&quot;&gt;{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years &lt;/math&gt;


The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps.

* [[Bully Mnemonic |Learn More About The Bully Mnemonic]]
* [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]]</text>
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[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Earth_Gravity_Calculator.html Earth Gravity Calculator (GitHub)]&lt;br /&gt;

[[File:TR_at_Bull_Moose_convention_1912.jpg|thumb|right|300px| The term [[w:Bullypulpit|bully pulpit]], meaning &quot;superb&quot; or &quot;wonderful&quot;, was coined by United States President [[w:Theodore Roosevelt|Theodore Roosevelt]], founder of the [[w:Bull Moose Party|Bull Moose Party]].

Six base units are defined in the '''Bully Metric''' system. Two variants of the '''apan''' are defined as [[w:Spacetime spacetime units]]. Three variants of the '''nat''' are defined as transformation units.  And the symbol '''&quot;e&quot;''' is used to represent elementary charge (the charge of a single electron).

The Bully Metric system was named in honor of actor Robin Williams' portrayal of US president Teddy Roosevelt.  Roosevelt frequently used of the word &quot;bully&quot; and coined the phrase &quot;bully pulpit&quot;.  As noted in Merriam-Webster's dictionary, bully had a positive connotation through much of history.  
{{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'.  Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker&lt;ref&gt;(Merriam-Webster. (n.d.). Bully. In Merriam-Webster.com dictionary. Retrieved May 16, 2024, from https://www.merriam-webster.com/dictionary/bully)&lt;/ref&gt;.}}
Bully spacetime units were designed to align with the orbital periods of various Solar System bodies. In particular, the number of seconds in Earth's sidereal year is [[Bully Mnemonic |31558150 s = 10330 * 3055 s]].  Large astronomical objects, such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn, can be thought of as bullies both in the traditional meaning of &quot;beautiful&quot;, but also in the modern meaning of being intimidating and threatening. The bullies, in Bully Metric, are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].

[[Bully_Metric_Foundations|The Foundations of Bully Metric]]&lt;br /&gt;
[[Bully_Metric_Astronomical_Coordinates|Bully Metric Coordinate System]]

== Spacetime Units ==

 ta = 30.55 femtoseconds (exact)
 
 la = [https://pml.nist.gov/cgi-bin/cuu/Value?c c] × 30.55 femtoseconds (exact)
    = [https://www.google.com/search?q=c+*+%2830.55e-15+s%29 9.1586595919 micrometers] (exact)

[[File:Bully_Metric_WGS_84_latitude_plot.png|thumb|right|300px|The change in gravitational (GR) time dilation (in parts per billion) relative to the North Pole as one moves from Earth's North Pole to the equator at sea level. This plot also shows the Bully Metric gravity &quot;g&quot; value in c/Zta at various call-out points. Special relativistic effects (SR) are not shown in the plot.]]

The '''time apan''' (or timepan) (symbol '''ta''') is by definition exactly 30.55 femtoseconds. The '''length apan''' (or lightpan or lengthpan) (symbol '''la''') is by definition the distance light travels in vacuum in 30.55 femtoseconds.  The scale of the Apan was selected so that the age and diameter of the visible Universe are approximately thirty orders of magnitude larger than the Apan, whereas the Planck time and Planck length are approximately thirty orders of magnitude smaller than the Apan.

Bully spacetime units were designed to leverage a [[Bully Metric Length Apan per Time Apan Squared|unique feature of Earth]]. Of all the planets in the cosmos, our Earth is unique in that the gravity on Earth's surface is approximately equal to the speed of light divided by one Earth year:

:&lt;math&gt;g \approx \frac{c}{P}&lt;/math&gt;

(where &lt;math&gt;g&lt;/math&gt; is surface gravity, &lt;math&gt;c&lt;/math&gt; is the speed of light, and &lt;math&gt;P&lt;/math&gt; is the orbital period).

In the Bully Metric system, a zetta-time-apan (Zta) has a duration of 30,550,000 seconds. The duration of a sidereal year is thus 1.033 zetta-time-apan (1.033 Zta), and the length of a sidereal light year is 1.033 zetta-length-apan (1.033 Zla). The speed of light in Bully Metric units is: 1.00 c = 1.00 Zla/Zta = 1.00 la/ta.  And the Bully Metric unit of gravity is: 1.00 g = 1.00 c/Zta. Gravity at sea level on Earth's surface varies from 1.001925 c/Zta at the North Pole to 0.996648 c/Zta at the equator.

The unit value of 30.55 femtoseconds was selected for the following five reasons:

# Approximate divisor of the ratio of the speed of light with g_earth: [https://www.google.com/search?q=c+%2F+g_earth+in+megaseconds c / g_earth ≈ 30.55 Ms]
# A divisor of Earth's sidereal year: [[Bully Mnemonic |31558150 s = 10330 × 3055 s]].
# Approximate divisor of the Great Year: [https://www.google.com/search?q=16%5E7+*+3055+s 1 Great Year ≈ 16&lt;sup&gt;7&lt;/sup&gt; × 3055 s]
# Approximate divisor of galactic year: [https://www.google.com/search?q=16%5E10+*+2+*+3055+s 1 galactic year ≈ 16&lt;sup&gt;10&lt;/sup&gt; × 2 × 3055 s]
# The light apan is an approximate divisor of [https://en.wikiversity.org/w/index.php?title=Bully_Metric#Traditional_Units multiple traditional length units].

&lt;br/&gt;[[Bully Metric Time Apan|The Bully Metric time unit]] &lt;br/&gt; [[Bully Metric Length Apan|The Bully Metric length unit]] &lt;br/&gt; [[Bully Metric Length Apan per Time Apan|The Bully Metric speed unit]] &lt;br/&gt; [[Bully Metric Length Apan per Time Apan Squared|The Bully Metric acceleration unit]]

== Transformation and Charge Units ==

 Rn ≈ (c&lt;sup&gt;3&lt;/sup&gt; / [https://pml.nist.gov/cgi-bin/cuu/Value?bg G]) (approximate)
    ≈ [https://www.google.com/search?q=c%5E3+%2F++G+in+kg+%2F+s 4.0370 × 10&lt;sup&gt;35&lt;/sup&gt; kilogram / second] (approximate)
 
 En = [https://pml.nist.gov/cgi-bin/cuu/Value?k 1.380649 x 10&lt;sup&gt;-23&lt;/sup&gt; joule / kelvin] (exact)
 
 An = 4 / (2π × K&lt;sub&gt;J&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt; × R&lt;sub&gt;J&lt;/sub&gt;)  (exact)
    = [https://www.google.com/search?q=4+%2F+%28+%282+*+pi+*+%28483%2C597.84841698+Ghz+%2F+V%29%5E2+*+%2825812.8074593+%CE%A9%29%29 1.05457182 × 10&lt;sup&gt;-34&lt;/sup&gt; joule second] (approximate)
 
 e = 2 / (K&lt;sub&gt;J&lt;/sub&gt; × R&lt;sub&gt;J&lt;/sub&gt;) (exact)
   = [https://www.google.com/search?q=2+%2F+%28+%28483%2C597.84841698+Ghz+%2F+V%29+*+%2825812.8074593+%CE%A9%29%29 1.60217663 × 10&lt;sup&gt;-19&lt;/sup&gt; coulombs] (approximate)

{| class=&quot;wikitable floatright&quot;
|+Table 1: Gravitational Mass
|-
! Body
! colspan=&quot;2&quot;|'''''mass'''''
|-
| Sun
| style=&quot;border-right:none;&quot;|{{val|161227199.623|(5)}}
| style=&quot;border-left :none;&quot;| Rn ta
|-
| Earth
| style=&quot;border-right:none;&quot;|{{val|484.2442275|(10)}}
| style=&quot;border-left :none;&quot;| Rn ta
|-
| Moon
| style=&quot;border-right:none;&quot;|{{val|5.9587358|(11)}}
| style=&quot;border-left :none;&quot;| Rn ta
|}

The '''rapinat''' (natural unit of [[w:Rapidity|rapidity]]) (symbol '''Rn''') is defined such that an object with a [[w:Standard gravitational parameter|standard gravitational parameter]] equal to the speed of light in vacuum cubed multiplied by 30.55 femtoseconds, will have a gravitational mass of one rapinat timepan.  The dwarf planet Pluto has a gravitational mass of roughly one rapinat timepan.  Earth's moon has a gravitational mass of approximately six rapinat timepan.  It would take roughly six Pluto sized objects smashed together to form something with the mass of the Earth's moon.  The first three digits of the Earth's mass can be approximated using the following: 1 Rn kta / (2 * 1.033) = 484 Rn ta. A few example masses are shown in Table 1.

The '''infonat''' (natural unit of [[w:Entropy|entropy]]) (symbol '''En''') is defined such that for an ideal gas in a given [[w:Microstate (statistical mechanics)|macrostate]], the entropy of the gas divided by the natural logarithm of the number of real microstates would be equivalent to one infonat.

{| class=&quot;wikitable floatright&quot;
|+Table 2: Quantum Rest Energy
|-
! Particle
! colspan=&quot;2&quot;|'''''rest energy'''''
|-
| Neutron
| style=&quot;border-right:none;&quot;|{{val|43608632955}}
| style=&quot;border-left :none;&quot;| An / ta
|-
| Proton
| style=&quot;border-right:none;&quot;|{{val|43548604715}}
| style=&quot;border-left :none;&quot;| An / ta
|-
| Electron
| style=&quot;border-right:none;&quot;|{{val|23717311.411}}
| style=&quot;border-left :none;&quot;| An / ta
|-
| Neutrino
| style=&quot;border-right:none;&quot;|&lt; {{val|5.57}}
| style=&quot;border-left :none;&quot;| An / ta
|-
| Graviton
| style=&quot;border-right:none;&quot;|&lt; {{val|3.6}}
| style=&quot;border-left :none;&quot;| An / Zta
|}
The '''actionat''' (natural unit of [[w:Action (physics) action]]) (symbol '''An'''), and '''elementary charge''' (symbol '''e'''), are defined such that if a Josephson Junction were exposed to microwave radiation of frequency 2 / 30.55 picoseconds (≈ [https://www.google.com/search?q=2+%2F+%2830.55+picoseconds%29 65.4664484 gigahertz]), then the junction would form equidistant Shapiro steps with separation of 2π actionats per kilo-time-apan electron.  Also,the quantum Hall effect will have resistance steps of multiples of 2π actionats per electron squared.  A few example rest energies are listed in Table 2.

[[Bully Metric Rapinat|The Bully Metric rapidity unit]]

== Normalized Physical Constants == 

The definitions of the Bully Metric system ensure normalization of the speed of light (c), Newton's gravitational constant (G), the Boltzmann constant (k&lt;sub&gt;B&lt;/sub&gt;), the reduced Planck constant (ħ), and the elementary charge (e):

&lt;math&gt;c = 1.0 \, \frac{la}{ta}&lt;/math&gt; (exact)

&lt;math&gt;G = 1.0 \, \frac{{la}^{3}}{Rn \, ta^{3}}&lt;/math&gt;  (exact)

&lt;math&gt;k_{B} = 1.0 \, En&lt;/math&gt; (exact)

&lt;math&gt;\hbar = 1.0 \, An&lt;/math&gt; (exact)

&lt;math&gt;elementary \, charge = 1.0 \, e &lt;/math&gt;  (exact)

= Physics Applications =

[[Bully Metric Bohr Model|The Bohr Atomic Model using Bully Metric units]]&lt;br/&gt;

= Planck units and the Bully Metric =
Table 3 below was taken from the Wikipedia [[w:Planck|units#History and definition|Planck units]] article:
{| class=&quot;wikitable&quot; style=&quot;margin:1em auto 1em auto; background:#fff; {{text color default}};&quot;
|+Table 3: Modern values for Planck's original choice of quantities
|-
 ! Name
 ! Expression
 ! Value ([[w:International System of Units SI]] units)
|- style=&quot;text-align:left;&quot;
 | Planck time
 | &lt;math&gt;t_\text{P} = \sqrt{\frac{\hbar G}{c^5}}&lt;/math&gt;
 | 5.391247(60)×10&lt;sup&gt;−44&lt;/sup&gt; s
|-
 | Planck length
 | &lt;math&gt;l_\text{P} = \sqrt{\frac{\hbar G}{c^3}}&lt;/math&gt;
 | 1.616255(18)×10&lt;sup&gt;−35&lt;/sup&gt; m
|-
 | Planck mass
 | &lt;math&gt;m_\text{P} = \sqrt{\frac{\hbar c}{G}}&lt;/math&gt;
 | 2.176434(24)×10&lt;sup&gt;-8&lt;/sup&gt; kg
|-
 | Planck temperature
 | &lt;math&gt;T_\text{P} = \sqrt{\frac{\hbar c^5}{G k_\text{B}^2}}&lt;/math&gt;
 | 1.416784(16)×10&lt;sup&gt;32&lt;/sup&gt; K
|}

=== Planck to Bully conversion constant ===
Since c, G, k&lt;sub&gt;B&lt;/sub&gt;, and ħ are all normalized in the Bully system, this ensures that Bully units have a simple relationship with Planck's units.  In fact, multiplying each value from Table 3 by 0.566660, results in the corresponding Bully value multiplied by 10&lt;sup&gt;-30&lt;/sup&gt;:

 0.566660 × t&lt;sub&gt;P&lt;/sub&gt; = 1.00001(11) × 10&lt;sup&gt;-30&lt;/sup&gt; ta
 0.566660 × l&lt;sub&gt;P&lt;/sub&gt; = 1.00001(11) × 10&lt;sup&gt;-30&lt;/sup&gt; la
 0.566660 × m&lt;sub&gt;P&lt;/sub&gt; = 1.00001(11) × 10&lt;sup&gt;-30&lt;/sup&gt; Rn ta

Table 4 below uses algebraic substitution to illustrate that there is one unique multiplicative constant that converts between Planck and Bully values. When Planck energy is included in the table (see &quot;Planck energy&quot; row in Table 4), one finds that the Planck to Bully conversion factor for energy is the inverse of the mass, time, and length conversion factor.

{| class=&quot;wikitable&quot; style=&quot;margin:1em auto 1em auto; background:#fff; {{text color default}};&quot;
|+Table 4: Planck's units relationship with Bully units
|-
 ! Name
 ! Expression
|-
 | Planck time
 | &lt;math&gt;t_\text{P} = \sqrt{\frac{\hbar G}{c^5}} = \sqrt{\frac{An \frac{la^{3}}{ Rn \, ta^{3}}}{\frac{la^{5}}{ta^{5}}}} = \sqrt{\frac{An}{Rn\,la^{2}}}\,ta&lt;/math&gt;
|-
 | Planck length
 | &lt;math&gt;l_\text{P} = \sqrt{\frac{\hbar G}{c^3}} = \sqrt{\frac{An \frac{la^{3}}{ Rn \, ta^{3}}}{\frac{la^{3}}{ta^{3}}}} = \sqrt{\frac{An}{Rn\,la^{2}}}\,la&lt;/math&gt;
|-
 | Planck mass
 | &lt;math&gt;m_\text{P} = \sqrt{\frac{\hbar c}{G}} = \sqrt{\frac{An \frac{la}{ta}}{\frac{la^{3}}{ Rn \, ta^{3}}}} = \sqrt{\frac{An}{Rn\,la^{2}}}\,Rn\,ta&lt;/math&gt;
|-
 | Planck energy
 | &lt;math&gt;m_\text{P} c^{2} = \sqrt{\frac{\hbar {c^5}}{G}} = \sqrt{\frac{An \frac{la^{5}}{ta^{5}}}{\frac{la^{3}}{ Rn \, ta^{3}}}} = \sqrt{\frac{ Rn \, la^{2}}{An}} \, \frac{An}{ta}&lt;/math&gt;
|-
 | Planck temperature
 | &lt;math&gt;T_\text{P} \times k_\text{B} = m_\text{P} c^{2} = \sqrt{\frac{ Rn \, la^{2}}{An}} \, \frac{An}{ta}&lt;/math&gt;
|- style=&quot;text-align:center;&quot;
 | ∴ 
 | &lt;math&gt;\frac{t_\text{P}}{ta} = \frac{l_\text{P}}{la} = \frac{m_\text{P}}{Rn\,ta} = \frac{\frac{An}{ta}}{m_\text{P} c^{2}} = \sqrt{\frac{An}{ Rn\,la^{2}}}&lt;/math&gt;
|}

=== The meaning of Planck units ===
The Planck length and time are understood to represent the smallest meaningful size of each quantity. Looking at small objects through a microscope requires energy.  If one were to build a microscope powerful enough to see objects at Planck length or smaller, the microscope would use so much energy that a black hole would form. In fact, the existence of objects on the Planck scale would cause a black hole.

Unlike the Planck length and time, the Planck mass of 2.176434(24)×10&lt;sup&gt;-8&lt;/sup&gt; kg is not a minimum value, but rather, it is a crossover point.  The Planck mass represents the boundary between gravitation and quantum mechanics.  If an object has a mass much larger than the Planck mass then gravitational effects will become more important.  If the mass is much smaller than the Planck mass then quantum mechanical effects will be more important.

=== Visible universe and the Bully Metric ===
The scale of the Apan was selected so that the age and diameter of the visible Universe are approximately thirty orders of magnitude larger than the Apan, whereas the Planck time and Planck length are approximately thirty orders of magnitude smaller than the Apan.  The universe is currently understood to be 13.7 billion years old, which is 14.15 × 10&lt;sup&gt;30&lt;/sup&gt; ta in Bully units. The radius of the visible universe is 46.508 billion light years, which is 48.04 × 10&lt;sup&gt;30&lt;/sup&gt; la in Bully units.

= The apan prefix table =
SI prefixes have the same meaning and conventions when used with apan variants as they have when used with standard SI units. See Table 5 below for the list of SI prefixes used with apan variants.  Also shown in the table are the smallest (Planck scale) and largest (Visible Universe) values for each unit.

{| class=&quot;wikitable&quot; style=&quot;padding: 0; text-align: center; width: 0; white-space: nowrap;&quot;
|+Table 5: The apan prefix table
|-
! colspan=3| Prefix
! colspan=3| Spacetime Symbols
|-
! Name !! Symbol !!  Base 10 !! Time !! Length !! Charge
|-
! colspan=3| Maximum Value &lt;br/&gt; (Observable Universe) || &lt;math&gt; 14.15 \, Qta&lt;/math&gt; || &lt;math&gt; 48.04 \, Qla&lt;/math&gt; || — 
|-
| quetta || Q || 10&lt;sup&gt;30&lt;/sup&gt; || Qta || Qla || Qe
|-
| ronna || R || 10&lt;sup&gt;27&lt;/sup&gt; || Rta || Rla || Re
|-
| yotta || Y || 10&lt;sup&gt;24&lt;/sup&gt; || Yta || Yla || Ye
|-
| zetta || Z || 10&lt;sup&gt;21&lt;/sup&gt; || Zta || Zla || Ze
|-
| exa || E || 10&lt;sup&gt;18&lt;/sup&gt; || Eta || Ela || Ee
|-
| peta || P || 10&lt;sup&gt;15&lt;/sup&gt; || Pta || Pla || Pe
|-
| tera || T || 10&lt;sup&gt;12&lt;/sup&gt; || Tta || Tla || Te
|-
| giga || G || 10&lt;sup&gt;9&lt;/sup&gt; || Gta || Gla || Ge
|-
| mega || M || 10&lt;sup&gt;6&lt;/sup&gt; || Mta || Mla || Me
|-
| kilo || k || 10&lt;sup&gt;3&lt;/sup&gt; || kta || kla || ke
|-
| — || — || 10&lt;sup&gt;0&lt;/sup&gt; || ta || la || e
|-
| milli || m || 10&lt;sup&gt;−3&lt;/sup&gt; || mta || mla || me
|-
| micro || μ || 10&lt;sup&gt;−6&lt;/sup&gt; || μta || μla || μe
|-
| nano || n || 10&lt;sup&gt;−9&lt;/sup&gt; || nta || nla || ne
|-
| pico || p || 10&lt;sup&gt;−12&lt;/sup&gt; || pta || pla || pe
|-
| femto || f || 10&lt;sup&gt;−15&lt;/sup&gt; || fta || fla || fe
|-
| atto || a || 10&lt;sup&gt;−18&lt;/sup&gt; || ata || ala || ae
|-
| zepto || z || 10&lt;sup&gt;−21&lt;/sup&gt; || zta || zla || ze
|-
| yocto || y || 10&lt;sup&gt;−24&lt;/sup&gt; || yta || yla || ye
|-
| ronto || r || 10&lt;sup&gt;−27&lt;/sup&gt; || rta || rla || re
|-
| quecto || q || 10&lt;sup&gt;−30&lt;/sup&gt; || qta || qla || qe
|-
! colspan=3| Minimum value &lt;br /&gt;(Planck Scale) || &lt;math&gt;\frac{qta}{0.566660}&lt;/math&gt; || &lt;math&gt;\frac{qla}{0.566660}&lt;/math&gt; || — 
|}

= The Mass/Momentum/Energy prefix table =
Mass, Momentum, and Energy are compound units in the Bully system.  Table 6 below lists SI prefixes used with the rapinat for gravitational masses, and with the actionat for quantum mechanical masses. Also shown in the table is the Planck scale cross-over value where gravitational and quantum effects meet.

{| class=&quot;wikitable&quot; style=&quot;padding: 0; text-align: center; width: 0; white-space: nowrap;&quot;
|+Table 6: The Mass/Momentum/Energy prefix table
|-
! colspan=3| Prefix
! colspan=3| Bully Metric Symbols
|-
! Name !! Symbol !! Base 10 !! Mass !! Momentum !! Energy
|-
| quetta || Q || 10&lt;sup&gt;30&lt;/sup&gt; || Rn Qta || Rn Qla || Rn c Qla
|-
! colspan=6| Observable Universe Mass = 480 Rn Rta
|-
| ronna || R || 10&lt;sup&gt;27&lt;/sup&gt; || Rn Rta || Rn Rla || Rn c Rla
|-
| yotta || Y || 10&lt;sup&gt;24&lt;/sup&gt; || Rn Yta || Rn Yla || Rn c Yla
|-
| zetta || Z || 10&lt;sup&gt;21&lt;/sup&gt; || Rn Zta || Rn Zla || Rn c Zla
|-
| exa || E || 10&lt;sup&gt;18&lt;/sup&gt; || Rn Eta || Rn Ela || Rn c Ela
|-
| peta || P || 10&lt;sup&gt;15&lt;/sup&gt; || Rn Pta || Rn Pla || Rn c Pla
|-
| tera || T || 10&lt;sup&gt;12&lt;/sup&gt; || Rn Tta || Rn Tla || Rn c Tla
|-
| giga || G || 10&lt;sup&gt;9&lt;/sup&gt; || Rn Gta || Rn Gla || Rn c Gla
|-
| mega || M || 10&lt;sup&gt;6&lt;/sup&gt; || Rn Mta || Rn Mla || Rn c Mla
|-
| kilo || k || 10&lt;sup&gt;3&lt;/sup&gt; || Rn kta || Rn kla || Rn c kla
|-
! colspan=6| Earth Mass = 484 Rn ta
|-
| — ||  || 10&lt;sup&gt;0&lt;/sup&gt; || Rn ta || Rn la || Rn c la
|-
| milli || m || 10&lt;sup&gt;−3&lt;/sup&gt; || Rn mta || Rn mla || Rn c mla
|-
| micro || μ || 10&lt;sup&gt;−6&lt;/sup&gt; || Rn μta || Rn μla || Rn c μla
|-
| nano || n || 10&lt;sup&gt;−9&lt;/sup&gt; || Rn nta || Rn nla || Rn c nla
|-
| pico || p || 10&lt;sup&gt;−12&lt;/sup&gt; || Rn pta || Rn pla || Rn c pla
|-
| femto || f || 10&lt;sup&gt;−15&lt;/sup&gt; || Rn fta || Rn fla || Rn c fla
|-
| atto || a || 10&lt;sup&gt;−18&lt;/sup&gt; || Rn ata || Rn ala || Rn c ala
|-
| zepto || z || 10&lt;sup&gt;−21&lt;/sup&gt; || Rn zta || Rn zla || Rn c zla
|-
| yocto || y || 10&lt;sup&gt;−24&lt;/sup&gt; || Rn yta || Rn yla || Rn c yla
|-
| ronto || r || 10&lt;sup&gt;−27&lt;/sup&gt; || Rn rta || Rn rla || Rn c rla
|-
| quecto || q || 10&lt;sup&gt;−30&lt;/sup&gt; || Rn qta || Rn qla || Rn c qla
|-
! rowspan=2 ! colspan=3| Crossover value &lt;br /&gt;(Planck Scale)&lt;br/&gt; (21.765 micro-grams) || &lt;math&gt;\frac{Rn \, qta}{0.566660}&lt;/math&gt; || &lt;math&gt;\frac{Rn \, qla}{0.566660}&lt;/math&gt; || &lt;math&gt;\frac{Rn \, c \, qla}{0.566660}&lt;/math&gt;
|-
!  &lt;math&gt;\frac{0.566660 \, An}{c \, qla}&lt;/math&gt; || &lt;math&gt;\frac{0.566660 \, An}{qla}&lt;/math&gt; || &lt;math&gt;\frac{0.566660 \, An}{qta}&lt;/math&gt;
|-
| quecto || q || 10&lt;sup&gt;−30&lt;/sup&gt; || An / c qla || An / qla || An / qta
|-
| ronto || r || 10&lt;sup&gt;−27&lt;/sup&gt; || An / c rla || An / rla || An / rta
|-
| yocto || y || 10&lt;sup&gt;−24&lt;/sup&gt; || An / c yla || An / yla || An / yta
|-
| zepto || z || 10&lt;sup&gt;−21&lt;/sup&gt; || An / c zla || An / zla || An / zta
|-
| atto || a || 10&lt;sup&gt;−18&lt;/sup&gt; || An / c ala || An / ala || An / ata
|-
| femto || f || 10&lt;sup&gt;−15&lt;/sup&gt; || An / c fla || An / fla || An / fta
|-
| pico || p || 10&lt;sup&gt;−12&lt;/sup&gt; || An / c pla || An / pla || An / pta
|-
| nano || n || 10&lt;sup&gt;−9&lt;/sup&gt; || An / c nla || An / nla || An / nta
|-
| micro || μ || 10&lt;sup&gt;−6&lt;/sup&gt; || An / c μla || An / μla || An / μta
|-
| milli || m || 10&lt;sup&gt;−3&lt;/sup&gt; || An / c mla || An / mla || An / mta
|-
! colspan=6| 1.00 electronvolt = 46.414 An / ta
|-
| — ||  || 10&lt;sup&gt;0&lt;/sup&gt; || An / c la || An / la || An / ta
|-
| kilo || k || 10&lt;sup&gt;3&lt;/sup&gt; || An / c kla || An / kla || An / kta
|-
| mega || M || 10&lt;sup&gt;6&lt;/sup&gt; || An / c Mla || An / Mla || An / Mta
|-
| giga || G || 10&lt;sup&gt;9&lt;/sup&gt; || An / c Gla || An / Gla || An / Gta
|-
| tera || T || 10&lt;sup&gt;12&lt;/sup&gt; || An / c Tla || An / Tla || An / Tta
|-
| peta || P || 10&lt;sup&gt;15&lt;/sup&gt; || An / c Pla || An / Pla || An / Pta
|-
| exa || E || 10&lt;sup&gt;18&lt;/sup&gt; || An / c Ela || An / Ela || An / Eta
|-
| zetta || Z || 10&lt;sup&gt;21&lt;/sup&gt; || An / c Zla || An / Zla || An / Zta
|-
| yotta || Y || 10&lt;sup&gt;24&lt;/sup&gt; || An / c Yla || An / Yla || An / Yta
|-
| ronna || R || 10&lt;sup&gt;27&lt;/sup&gt; || An / c Rla || An / Rla || An / Rta
|-
| quetta || Q || 10&lt;sup&gt;30&lt;/sup&gt; || An / c Qla || An / Qla || An / Qta
|}

= Traditional Units =

[[File:Vitruvian_Distance.png|500px]]

Bully variations of traditional units of measure may be accepted for use within the Bully system, provided the Bully definition is a simple integer multiple of Bully base units. The Bully definition shall not be used in contexts which cause confusion with the competing traditional unit, in cases where the traditional unit is still in use.

The following definitions are accepted for use within the Buly system:

* 1 Bully Mile = 200 megapan ([https://www.google.com/search?q=200000000+*+c+*+30.55+fs+in+nautical+miles 0.9891 nautical miles])
* 1 Bully Fathom = 200 kilopan ([https://www.google.com/search?q=200000+*+c+*+30.55+fs+in+inches 72.115 inches])
* 1 Bully Yard = 100 kilopan ([https://www.google.com/search?q=100000+*+c+*+30.55+fs+in+inches 36.058 inches])
* 1 Bully Cubit = 50 kilopan ([https://www.google.com/search?q=50000+*+c+*+30.55+fs+in+inches 18.029 inches])
* 1 Bully Span = 25 kilopan ([https://www.google.com/search?q=25000+*+c+*+30.55+fs+in+inches 9.014 inches])
* 1 Bully Yard&lt;sup&gt;3&lt;/sup&gt; = 200 Bully Gallons ([https://www.google.com/search?q=100%5E3+*+%281000+*+c+*+30.55+fs%29%5E3+in+quarts 811.78 US quarts])
* 1 Bully Cubit&lt;sup&gt;3&lt;/sup&gt; = 25 Bully Gallons ([https://www.google.com/search?q=50%5E3+*+%281000+*+c+*+30.55+fs%29%5E3+in+quarts 101.47 US quarts])
* 1 Bully Gallon = 5,000 kilopan&lt;sup&gt;3&lt;/sup&gt; ([https://www.google.com/search?q=5000+*+%281000+*+c+*+30.55+fs%29%5E3+in+quarts 4.059 US quarts])
* 1 Bully Spoon = 20 kilopan&lt;sup&gt;3&lt;/sup&gt; ([https://www.google.com/search?q=20+*+%281000+*+c+*+30.55+fs%29%5E3+in+tablespoon 1.039 US tablespoons])
* 1 Bully Dash = 1 kilopan&lt;sup&gt;3&lt;/sup&gt; ([https://www.google.com/search?q=1+*+%281000+*+c+*+30.55+fs%29%5E3+in+milliliter 0.7682 milliliter])
* 1 Bully Stone = 500 Rn yta ([https://www.google.com/search?q=500+*+10%5E%28-24%29+*+30.55+fs+*+c%5E3+%2F++G+in+lbs 13.59477 pounds])

= References =</text>
      <sha1>3jmo7mqu7m84ec20lfxqnzj2j4t6569</sha1>
    </revision>
  </page>
  <page>
    <title>User:Tommy Kronkvist</title>
    <ns>2</ns>
    <id>320737</id>
    <revision>
      <id>2815787</id>
      <parentid>2815644</parentid>
      <timestamp>2026-06-15T06:54:35Z</timestamp>
      <contributor>
        <username>Tommy Kronkvist</username>
        <id>31941</id>
      </contributor>
      <comment>User statistics.</comment>
      <origin>2815787</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2646" sha1="7cg7xfrri07sn6655j3uvt597d8rz1x" xml:space="preserve">&lt;div style=&quot;margin: 0 0 1em 0;&quot;&gt;{{userpage}}&lt;/div&gt;
{{Userboxtop|toptext=Babel:}}
{{#babel:sv|en-4|de-2|la-1}}
{{Userboxbottom}}
[[File:Sorbus torminalis Trunk and canopy.jpg|thumb|310px|The intracanopy of a Wild Service Tree, i.e. &lt;small&gt;''Torminalis glaberrima'' (Gand.) Sennikov &amp; Kurtto, ''Memoranda Soc. Fauna Fl. Fenn.'' 93: 32 (2017).&lt;/small&gt;]]&lt;br /&gt;
 
Most of my wiki contributions are made to [[:species:Main Page|Wikispecies]] where I'm an administrator, bureaucrat and interface admin,&lt;small&gt;&lt;sup&gt;[https://species.wikimedia.org/w/index.php?title=Special:ListUsers&amp;limit=1&amp;username=Tommy_Kronkvist (verify)]&lt;/sup&gt;&lt;/small&gt; to the Swedish Wikimedia Chapter [[WMSE:|Wikimedia Sverige]] (WMSE) where I'm an administrator,&lt;small&gt;&lt;sup&gt;(&lt;span class=&quot;plainlinks&quot;&gt;[https://se.wikimedia.org/w/index.php?title=Special:Användare&amp;limit=1&amp;username=Tommy_Kronkvist verify]&lt;/span&gt;)&lt;/sup&gt;&lt;/small&gt; and as administrator and interface administrator at the Swedish version of [[wikivoyage:sv:Huvudsida|Wikivoyage]].&lt;small&gt;&lt;sup&gt;(&lt;span class=&quot;plainlinks&quot;&gt;[https://sv.wikivoyage.org/w/index.php?title=Special:ListUsers&amp;limit=1&amp;username=Tommy_Kronkvist verify]&lt;/span&gt;)&lt;/sup&gt;&lt;/small&gt;

So far (June 15, 2026), I've made just over 393,500 edits to 153 of the Wikimedia sister projects&amp;nbsp;– the majority of them to Wikispecies and Wikidata. My global account information for all of Wikimedia can be found [[meta:Special:CentralAuth/Tommy Kronkvist|here]].

Swedish is my mother tongue&amp;nbsp;– even though I was born in Finland&amp;nbsp;– but I feel comfortable speaking and writing English and to some extent in German as well. Odd as it may seem, unfortunately I can't speak any Finnish even though I went to school there for a few years prior to moving to Sweden (see [[w:Swedish-speaking population of Finland|Swedish-speaking population of Finland]] in Wikipedia). I've lived all over Sweden but nowadays reside in Uppsala, the fourth biggest city and former capital of Sweden.

I'm only the fourth generation named &quot;Kronkvist&quot;. My family name consists of two parts: ''kron'' – a short form of the Swedish word ''krona'' meaning 'crown', as in coronation crown or tree crown – and ''kvist'', meaning 'bough' or 'twig'. Hence the name ''Kronkvist'' refers to a twig in the canopy of a forest. I'm the fourth generation of Kronkvist's. Prior to that our family name was ''Mattus'': an oeconym meaning &quot;Matthew's Farm&quot;, dating back to at least 1637.
{{Clear}}
{{User committed identity|a6edd6d2fdbf82621f0cda4e5525c71f8da9b5dfd308242c3c63365e998c32c5406b75448380903265a5403edffd1a0435b61ac943f3c65870db9250f8b884a9|SHA-512|background=#e0e8ff|border=e0e8ff}}</text>
      <sha1>7cg7xfrri07sn6655j3uvt597d8rz1x</sha1>
    </revision>
  </page>
  <page>
    <title>Probability Dilation Theory</title>
    <ns>0</ns>
    <id>321584</id>
    <revision>
      <id>2815747</id>
      <parentid>2815580</parentid>
      <timestamp>2026-06-15T02:27:48Z</timestamp>
      <contributor>
        <username>Howie2024</username>
        <id>2995240</id>
      </contributor>
      <minor />
      <comment>/* Related literature on probabilistic dilation, conditioning behavior, geometric probability, and curvature-dependent probabilistic structure includes the following works: */</comment>
      <origin>2815747</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="36012" sha1="pijiyclqoh5c9nqnhxc20vneh0kpjlq" xml:space="preserve">{{Research project}}
{{Original research}}
{{To be peer reviewed}}


== Research abstract ==
'''Probability Dilation Theory (PDT)''' is a measure-theoretic research framework for studying how probability measures transform under '''positive reweighting (dilation)''' while preserving normalization and producing controlled changes in expectation values.

The theory is an exploratory framework for iterative probability-measure evolution under positive dilation fields. The framework studies how repeated probabilistic reweighting transformations may generate emergent statistical structure, entropy flow, and multiscale probability dynamics.

At its core, PDT studies how repeated positive probability reweighting transformations alter the long-term structure of probability distributions.
PDT treats a probability measure as the primary mathematical object and investigates:
* invariant identities induced by reweighting,
* composition and iteration of dilations,
* fixed points and near-fixed behavior,
* whether iterative measure updates can generate testable multiscale statistical structure (to be evaluated via explicit models and simulations).

PDT is presented as a mathematical framework. Any proposed application to physics or cosmology must be expressed as a concrete model (space, baseline measure, dilation field) and tested against falsifiable predictions.

== Overview ==
PDT is motivated by the observation that some structural information can be recovered from sampling statistics (e.g., [[w:Buffon's needle problem|Buffon’s needle]]). PDT abstracts this idea by focusing on measure transformation itself: a dilation field modifies a baseline probability measure in a way that is:
* mathematically well-defined (positivity and normalization),
* composable under iteration,
* analyzable for invariants and fixed points.
=== Conceptual interpretation ===

A simplified conceptual flow of the PDT framework is:

&lt;pre&gt;
Baseline probability measure P
            ↓
Positive dilation field D(x)
            ↓
Reweighted probability measure P~
            ↓
Observable statistical changes
&lt;/pre&gt;
Repeated dilation may qualitatively behave as:

&lt;pre&gt;
Broad initial distribution
        ↓
Localized reweighting
        ↓
Probability concentration
        ↓
Emergent multiscale structure
&lt;/pre&gt;

Different classes of dilation fields may therefore generate qualitatively different long-term probability dynamics.
In this interpretation, PDT does not alter the underlying sample space directly. Instead, it modifies how probability mass is distributed across that space through a positive reweighting field.

Regions with larger values of the dilation field contribute more strongly to the transformed measure, while normalization preserves total probability. Earlier exploratory formulations of Probability Dilation Theory (PDT) were informally referred to as the Einstein Buffon Process (EBP), reflecting initial probabilistic-geometric interpretations inspired by Buffon-type constructions and Einstein-style scaling analogies. The framework has since evolved toward a broader iterative theory of probability-measure dynamics under positive dilation fields. A simple iterative interpretation may also be visualized as:

&lt;pre&gt;
P₀
 ↓ D₁
P₁
 ↓ D₂
P₂
 ↓ D₃
P₃
 ↓ ⋯
&lt;/pre&gt;

where each dilation field reweights the probability structure generated by the previous step.

Different classes of dilation fields may therefore generate qualitatively different long-term probability dynamics.

= Mathematical framework =

== Definitions and notation ==
Let &lt;math&gt;(\Omega,\Sigma)&lt;/math&gt; be a measurable space.

* &lt;math&gt;P&lt;/math&gt; denotes a probability measure on &lt;math&gt;(\Omega,\Sigma)&lt;/math&gt;.
* If &lt;math&gt;P&lt;/math&gt; has a density &lt;math&gt;p&lt;/math&gt; with respect to a reference measure &lt;math&gt;\mu&lt;/math&gt;, then &lt;math&gt;dP=p\,d\mu&lt;/math&gt;.
* &lt;math&gt;D:\Omega\to(0,\infty)&lt;/math&gt; is a measurable '''dilation field''' (a positive weight function).
* &lt;math&gt;Z(P,D)&lt;/math&gt; is the normalization constant:
.&lt;math&gt;
Z(P,D)=\int_\Omega D\,dP
&lt;/math&gt;
* For an observable &lt;math&gt;f:\Omega\to\mathbb{R}&lt;/math&gt; integrable under the relevant measure,
&lt;math&gt;
\mathbb{E}_P[f]
=
\int_\Omega f\,dP
&lt;/math&gt;.

== PDT transformation (probability reweighting) ==

Given &lt;math&gt;P&lt;/math&gt; and &lt;math&gt;D&lt;/math&gt; with &lt;math&gt;0&lt;Z(P,D)&lt;\infty&lt;/math&gt;, define the '''PDT transform''' &lt;math&gt;\widetilde{P}=\mathrm{PDT}(P;D)&lt;/math&gt; by:

&lt;math&gt;
\widetilde{P}(A)
=
\frac{
\int_A D\,dP
}{
\int_\Omega D\,dP
}
\quad\text{for all }A\in\Sigma
&lt;/math&gt;

If &lt;math&gt;dP=p\,d\mu&lt;/math&gt;, then &lt;math&gt;d\widetilde{P}=\widetilde{p}\,d\mu&lt;/math&gt;, where

&lt;math&gt;
\widetilde{p}(x)
=
\frac{D(x)\,p(x)}{Z}
&lt;/math&gt;

and

&lt;math&gt;
Z
=
\int_\Omega D(x)\,p(x)\,d\mu
&lt;/math&gt;

'''Interpretation:''' the dilation field &lt;math&gt;D&lt;/math&gt; shifts probability mass toward regions where &lt;math&gt;D&lt;/math&gt; is larger, while renormalization keeps total probability equal to 1.

PDT is mathematically related to importance sampling, Gibbs-style reweighting, and Radon–Nikodym measure transformations, although the framework emphasizes compositional and geometric interpretations of probability reweighting rather than only numerical estimation procedures.

Unlike conventional importance sampling, however, PDT emphasizes the compositional and potentially dynamical behavior of repeated probability reweighting transformations.
A familiar physical example of a strictly positive factor is the Lorentz factor:

&lt;math&gt;
\gamma(v)
=
\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}
&lt;/math&gt;

for

&lt;math&gt;
|v|&lt;c
&lt;/math&gt;

Lorentz contraction for a rod of rest length &lt;math&gt;L_0&lt;/math&gt; moving at speed &lt;math&gt;v&lt;/math&gt; is:

&lt;math&gt;
L(v)=\frac{L_0}{\gamma(v)}
&lt;/math&gt;

To connect this idea to PDT (as an illustration only), one may define a positive dilation field based on &lt;math&gt;\gamma&lt;/math&gt;.

== Worked finite example ==

Consider a finite probability space:

&lt;math&gt;
\Omega=\{a,b,c\}
&lt;/math&gt;

with baseline probabilities:

&lt;math&gt;
P(a)=0.2,\quad
P(b)=0.3,\quad
P(c)=0.5
&lt;/math&gt;

Define a positive dilation field:

&lt;math&gt;
D(a)=1,\quad
D(b)=2,\quad
D(c)=4
&lt;/math&gt;

The normalization constant is:

&lt;math&gt;
Z=\sum_x D(x)P(x)
&lt;/math&gt;

giving:

&lt;math&gt;
Z=(1)(0.2)+(2)(0.3)+(4)(0.5)=2.8
&lt;/math&gt;

The PDT-transformed probabilities become:

&lt;math&gt;
\widetilde{P}(a)=\frac{0.2}{2.8}\approx0.071
&lt;/math&gt;

&lt;math&gt;
\widetilde{P}(b)=\frac{0.6}{2.8}\approx0.214
&lt;/math&gt;

&lt;math&gt;
\widetilde{P}(c)=\frac{2.0}{2.8}\approx0.714
&lt;/math&gt;

This illustrates how PDT shifts probability mass toward regions with larger dilation weights while preserving normalization.

== Composition of dilations ==

An important structural property of sequential PDT transformations is that compose multiplicatively.

Suppose two positive dilation fields:

&lt;math&gt;
D_1(x)&gt;0
&lt;/math&gt;

and

&lt;math&gt;
D_2(x)&gt;0
&lt;/math&gt;

are applied successively to a baseline probability measure &lt;math&gt;P&lt;/math&gt;.

The first dilation produces:

&lt;math&gt;
\widetilde{P}_1(A)
=
\frac{\int_A D_1\,dP}
{\int_\Omega D_1\,dP}
&lt;/math&gt;

Applying the second dilation field to &lt;math&gt;\widetilde{P}_1&lt;/math&gt; gives:

&lt;math&gt;
\widetilde{P}_2(A)
=
\frac{\int_A D_2\,d\widetilde{P}_1}
{\int_\Omega D_2\,d\widetilde{P}_1}
&lt;/math&gt;

Substituting the first transformation into the second yields:

&lt;math&gt;
\widetilde{P}_2(A)
=
\frac{
\int_A D_2D_1\,dP
}{
\int_\Omega D_2D_1\,dP
}
&lt;/math&gt;

This shows that sequential PDT transformations compose through multiplication of the dilation fields.

This compositional structure allows iterative probability reweighting to be studied using products of positive fields, potentially generating multiscale or hierarchical probability structures under repeated application.

== Fixed points and iterative dynamics ==

An important question in PDT concerns the long-term behavior of repeated PDT transformations.

Given an initial probability measure:

&lt;math&gt;
P_0
&lt;/math&gt;

and a sequence of positive dilation fields:

&lt;math&gt;
D_1,D_2,D_3,\dots
&lt;/math&gt;

successive PDT transformations generate a sequence of measures:

&lt;math&gt;
P_0
\rightarrow
P_1
\rightarrow
P_2
\rightarrow
P_3
\rightarrow \cdots
&lt;/math&gt;

where each transformed measure is obtained by reweighting the previous one.

A measure &lt;math&gt;P&lt;/math&gt; is called a fixed point of a dilation field &lt;math&gt;D&lt;/math&gt; if:

&lt;math&gt;
\widetilde{P}=P
&lt;/math&gt;

under the PDT transformation.

In the simplest case, this requires the dilation field to be constant almost everywhere with respect to &lt;math&gt;P&lt;/math&gt;. More general fixed-point behavior may arise when iterative compositions balance probability amplification against normalization.

More generally, repeated compositions of nontrivial dilation fields may generate:

* hierarchical probability structure;
* multiscale statistical behavior;
* attractor-like distributions;
* approximately stable transformed measures.

These questions connect PDT to broader areas of:

* dynamical systems;
* stochastic processes;
* iterative renormalization methods;
* probabilistic geometry.

At present these iterative properties remain largely unexplored within the PDT framework.

== Entropy and iterative probability flow ==

Repeated PDT transformations may alter the entropy structure of a probability measure.

For a discrete probability distribution:

&lt;math&gt;
P=\{p_i\}
&lt;/math&gt;

the Shannon entropy is:

&lt;math&gt;
H(P)
=
-\sum_i p_i \log p_i
&lt;/math&gt;

Under iterative PDT transformation, successive transformed measures:

&lt;math&gt;
P_0
\rightarrow
P_1
\rightarrow
P_2
\rightarrow \cdots
&lt;/math&gt;

may exhibit changing entropy behavior depending on the structure of the dilation fields.

For example:
* strongly localized dilation fields may concentrate probability mass and reduce entropy;
* broader or smoothing dilation fields may distribute probability more evenly and increase entropy;
* iterative compositions may generate approximately stable entropy profiles.

These questions connect PDT to:
* information theory,
* statistical mechanics,
* stochastic dynamics,
* and renormalization-style iterative systems.

At present the entropy behavior of iterative PDT transformations remains an open area for investigation.

== Toy experiment: entropy under repeated dilation ==

A simple finite-state experiment illustrates how repeated PDT transformations can change the entropy of a probability distribution.

Let the initial probability distribution be:

&lt;math&gt;
P_0=(0.2,0.2,0.2,0.2,0.2)
&lt;/math&gt;

and define a positive dilation field:

&lt;math&gt;
D=(1,1,2,4,8)
&lt;/math&gt;

At each step, apply the PDT update:

&lt;math&gt;
P_{n+1}(i)
=
\frac{D(i)P_n(i)}
{\sum_j D(j)P_n(j)}
&lt;/math&gt;

The Shannon entropy is:

&lt;math&gt;
H(P_n)
=
-\sum_i P_n(i)\log P_n(i)
&lt;/math&gt;

In this toy model, repeated dilation shifts probability mass toward the highest-weight state. Over ten iterations, the entropy decreases from approximately:

&lt;math&gt;
H(P_0)\approx1.6094
&lt;/math&gt;

to:

&lt;math&gt;
H(P_{10})\approx0.00775
&lt;/math&gt;

The final distribution is approximately:

&lt;math&gt;
P_{10}
\approx
(0.000000001,\;0.000000001,\;0.000000953,\;0.000975609,\;0.999023437)
&lt;/math&gt;

This example demonstrates probability concentration under repeated positive dilation. It is a finite-state toy model and should not be interpreted as physical evidence; its purpose is to illustrate iterative PDT behavior.
== Mathematical context ==
PDT transformations may be viewed as exploratory probability-measure reweighting procedures related conceptually to conditioning behavior, stochastic transformations, entropy evolution, and probabilistic dilation phenomena studied in imprecise probability theory and dynamical systems literature.
In PDT, the term ''dilation'' refers to probabilistic reweighting and transformation behavior under localized weighting fields rather than the formal operator-theoretic notion of dilation used in functional analysis.
The iterative entropy-flow experiments explored in PDT resemble finite-state dynamical systems in which repeated transformations generate convergence, concentration, and emergent probabilistic structure over successive iterations.
=== Example entropy evolution ===

{| class=&quot;wikitable&quot;
! Iteration !! Shannon entropy
|-
| 0 || 1.6094
|-
| 1 || 1.2990
|-
| 2 || 0.7790
|-
| 3 || 0.4399
|-
| 5 || 0.1500
|-
| 10 || 0.0078
|}
Entropy evolution under repeated localized PDT transformation showing entropy reduction and probability concentration under iterative probabilistic reweighting. Programmatically generated using Python in a ChatGPT-assisted workflow. The entropy decreases under repeated application of the dilation field as probability mass becomes increasingly concentrated in the highest-weight states.
=== Localized dilation fields ===

A useful class of PDT transformations is generated by localized positive dilation fields.

Consider a one-dimensional finite configuration space with states indexed by:

&lt;math&gt;
x=0,1,2,\dots,N
&lt;/math&gt;

and define a localized dilation field centered at &lt;math&gt;x_0&lt;/math&gt;:

&lt;math&gt;
D(x)
=
\exp\!\left(
\lambda
\exp\!\left(
-\frac{(x-x_0)^2}{2\sigma^2}
\right)
\right)
&lt;/math&gt;

where:

* &lt;math&gt;\lambda&gt;0&lt;/math&gt; controls the strength of the dilation;
* &lt;math&gt;\sigma&lt;/math&gt; controls the spatial width of the localized field.

Narrow values of &lt;math&gt;\sigma&lt;/math&gt; produce sharply localized amplification, while broader values produce smoother probability reweighting across the configuration space.

Under iterative PDT dynamics:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D(x)P_n(x)
}{
\sum_y D(y)P_n(y)
}
&lt;/math&gt;

the probability distribution may progressively concentrate near the center of the dilation field.

=== Example entropy evolution for localized fields ===

Using an initially uniform distribution over 21 states and iterating the PDT transformation 10 times produces the following representative entropy behavior:

{| class=&quot;wikitable&quot;
! Field width &lt;math&gt;\sigma&lt;/math&gt;
! Final entropy after 10 iterations
! Maximum probability after 10 iterations
|-
| 1.5 || 0.0352 || 0.9950
|-
| 3.0 || 0.8162 || 0.7141
|-
| 6.0 || 1.5367 || 0.3595
|}
[[File:PDT entropy evolution localized field.png|thumb|center|600px|Entropy evolution under repeated localized PDT transformation showing entropy reduction and probability concentration under iterative probabilistic reweighting.]]
[[File:Epd_entropy_evolution.png|thumb|center|600px|Entropy evolution under repeated localized PDT dilation. Narrow localized dilation fields produce rapid entropy reduction and probability concentration under iterative reweighting.]]
These results indicate that narrower localized dilation fields generate stronger probability concentration and more rapid entropy reduction.

== Comparative entropy-flow experiments ==

The following finite-state computational experiments illustrate comparative entropy evolution under several classes of PDT dilation fields. Each experiment begins with the same initially uniform probability distribution and applies repeated PDT transformations under different field structures. The experiments are exploratory and intended to illustrate qualitative differences in iterative probabilistic behavior rather than empirical physical predictions.
{| class=&quot;wikitable&quot;
|+ Comparative entropy-flow behavior under PDT field classes
! Field class
! Final entropy
! Entropy decrease
! Final max probability
! Qualitative behavior
|-
| Localized
| 0.3104
| 3.4032
| 0.9275
| Strong probability concentration
|-
| Oscillatory
| 1.5779
| 2.1357
| 0.3418
| Distributed oscillatory structure
|-
| Multi-peak
| 0.2851
| 3.4284
| 0.9425
| Multiple concentration regions
|-
| Stochastic
| 0.7744
| 2.9392
| 0.7413
| Fluctuating concentration behavior
|}
These experiments suggest that different classes of dilation fields may generate qualitatively distinct entropy-flow and concentration behavior under iterative PDT dynamics. Localized and multi-peak fields produce strong entropy reduction and probability concentration, while oscillatory fields preserve more distributed probabilistic structure. Stochastic fields exhibit fluctuating but still partially concentrating behavior in this finite-state example.
In this toy model, repeated localized dilation behaves qualitatively like an attractor centered on the highest-weight region of the configuration space.
[[File:Pdt comparative entropy flow.png|thumb|Comparative entropy evolution under localized, oscillatory, multi-peak, and stochastic PDT dilation fields.]]
The experiment is intended only as a finite-state demonstration of iterative PDT dynamics and should not be interpreted as physical evidence.

=== Oscillatory dilation fields ===

Another useful class of PDT transformations is generated by oscillatory positive dilation fields.

One example is:

&lt;math&gt;
D(x)
=
\exp(\lambda\sin(kx))
&lt;/math&gt;

where:

* &lt;math&gt;\lambda&gt;0&lt;/math&gt; controls the strength of the oscillatory amplification;
* &lt;math&gt;k&lt;/math&gt; controls the spatial frequency of the oscillation.

Because the exponential is always positive, the dilation field remains strictly positive for all states.

Unlike localized dilation fields, oscillatory fields may generate multiple competing high-weight regions across the configuration space.

Under repeated PDT transformation:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D(x)P_n(x)
}{
\sum_y D(y)P_n(y)
}
&lt;/math&gt;

probability mass may evolve toward several distributed concentration regions rather than a single dominant attractor.

=== Example oscillatory-field experiment ===

A finite-state experiment was performed using:

* 41 discrete states;
* an initially uniform probability distribution;
* a positive oscillatory dilation field with three spatial oscillation cycles;
* 10 successive PDT iterations.

Representative entropy behavior was:

{| class=&quot;wikitable&quot;
! Iteration
! Shannon entropy
|-
| 0 || 3.7136
|-
| 2 || 2.8699
|-
| 5 || 2.3018
|-
| 10 || 1.9335
|}

Unlike sharply localized dilation fields, the oscillatory field produced slower entropy reduction and multiple probability concentration peaks distributed across the configuration space.

After 10 iterations, the largest probability concentration remained distributed rather than collapsing into a single dominant state.

This suggests that different classes of positive dilation fields may generate qualitatively different long-term iterative probability structures.

The experiment is intended only as a finite-state demonstration of iterative PDT dynamics and should not be interpreted as physical evidence.
=== Multi-peak localized dilation fields ===

A broader class of PDT transformations may be generated using multiple localized dilation peaks distributed across the configuration space.

One example is:

&lt;math&gt;
D(x)
=
\exp\!\left(
\sum_k
\lambda_k
\exp\!\left(
-\frac{(x-x_k)^2}{2\sigma_k^2}
\right)
\right)
&lt;/math&gt;

where:

* &lt;math&gt;x_k&lt;/math&gt; are the locations of the dilation peaks;
* &lt;math&gt;\lambda_k&gt;0&lt;/math&gt; control the amplification strength of each peak;
* &lt;math&gt;\sigma_k&lt;/math&gt; control the spatial width of each localized region.

This construction generates a positive multimodal dilation landscape containing several competing amplification regions.

Under repeated PDT iteration:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D(x)P_n(x)
}{
\sum_y D(y)P_n(y)
}
&lt;/math&gt;

probability mass may evolve toward multiple partially localized concentration regions.

Unlike single localized dilation fields, multi-peak fields may generate:

* competing attractor-like regions;
* hierarchical probability concentration;
* partially stabilized multimodal distributions;
* multiscale probability structure.

Depending on the relative strengths and widths of the peaks, the iterative dynamics may favor:
* dominance by a single peak;
* coexistence of several concentration regions;
* or slowly evolving metastable probability structures.

=== Conceptual interpretation ===

A qualitative iterative evolution may be visualized as:

&lt;pre&gt;
Broad initial distribution
        ↓
Multiple localized amplifications
        ↓
Competing concentration regions
        ↓
Emergent multimodal probability structure
&lt;/pre&gt;

This class of dilation fields suggests that iterative PDT dynamics may generate richer probability organization than either single localized attractors or simple oscillatory fields alone.

At present these behaviors remain exploratory computational observations within finite-state toy models.
=== Random and stochastic dilation fields ===

Another important class of PDT transformations arises when the dilation field itself varies stochastically.

A simple stochastic dilation field may be written schematically as:

&lt;math&gt;
D_n(x)
=
\exp\!\left(
\sigma \eta_n(x)
\right)
&lt;/math&gt;

where:

* &lt;math&gt;\eta_n(x)&lt;/math&gt; is a random field or stochastic fluctuation at iteration &lt;math&gt;n&lt;/math&gt;;
* &lt;math&gt;\sigma&gt;0&lt;/math&gt; controls the strength of the stochastic variation.

Because the exponential is strictly positive, the dilation field remains positive for all realizations of the random process.

Under repeated PDT iteration:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D_n(x)P_n(x)
}{
\sum_y D_n(y)P_n(y)
}
&lt;/math&gt;

the probability landscape itself fluctuates dynamically from one iteration to the next.

Unlike deterministic localized or oscillatory dilation fields, stochastic dilation fields may generate:

* fluctuating concentration regions;
* transient attractor-like structures;
* noise-driven entropy evolution;
* intermittent probability concentration;
* metastable probabilistic configurations.

=== Conceptual interpretation ===

A qualitative stochastic evolution may be visualized as:

&lt;pre&gt;
Broad initial distribution
        ↓
Random localized amplification
        ↓
Fluctuating concentration regions
        ↓
Dynamic probabilistic structure
&lt;/pre&gt;

Depending on the stochastic process used to generate the dilation fields, the long-term dynamics may exhibit:
* partial concentration,
* persistent fluctuations,
* stochastic stabilization,
* or continuously evolving probabilistic structure.

These ideas connect PDT to broader areas of:
* stochastic processes;
* random multiplicative systems;
* statistical mechanics;
* noise-driven dynamical systems;
* probabilistic geometry.

At present these behaviors remain exploratory computational possibilities within finite-state toy models.

== Qualitative classes of iterative PDT behavior ==

Different classes of positive dilation fields may generate qualitatively different long-term probability dynamics under repeated PDT transformation.

The following table summarizes several representative classes explored within finite-state toy models.

{| class=&quot;wikitable&quot;
! Dilation-field class
! Typical iterative behavior
! Representative qualitative structure
|-
| Localized fields
| Strong entropy reduction and concentration toward a dominant region
| Single attractor-like concentration
|-
| Oscillatory fields
| Distributed amplification with slower entropy reduction
| Patterned multimodal structure
|-
| Multi-peak localized fields
| Competition between several concentration regions
| Hierarchical or metastable probability structure
|-
| Random and stochastic fields
| Fluctuating amplification and noise-driven evolution
| Dynamic probabilistic landscapes
|}

These examples suggest that iterative PDT reweighting may generate a broad spectrum of emergent statistical structures depending on the geometry and dynamics of the dilation field.

Within the PDT framework, the iterative behavior of probability measures may therefore depend as strongly on the structure of the dilation field as on the initial probability distribution itself.

At present these qualitative behaviors remain exploratory computational observations within finite-state toy models.

== Numerical simulation and iterative models ==

=== Simulation model description ===

In discrete demonstrations, the “state space” may be represented by a finite set such as bins, configurations, or catalog points.

Two equivalent discrete implementations are common:

* '''weighted evaluation''': retain all points and assign weights proportional to &lt;math&gt;D&lt;/math&gt;;
* '''importance resampling''': generate a new empirical catalog with sampling probabilities proportional to &lt;math&gt;D&lt;/math&gt;.

=== Demonstration: reweighting mock galaxy catalogs ===

A simple computational demonstration of PDT may be constructed using synthetic galaxy catalogs in a periodic simulation box.

The demonstration pipeline is:

# generate a baseline mock catalog;
# define a positive dilation field over the configuration space;
# perform PDT-style importance resampling;
# compute the resulting two-point correlation function &lt;math&gt;\xi(r)&lt;/math&gt;;
# compare transformed and baseline catalogs.

One example dilation field is:

&lt;math&gt;
D(x)=\exp(\lambda\phi(x))
&lt;/math&gt;

where:

* &lt;math&gt;\lambda&gt;0&lt;/math&gt; controls the strength of the dilation;
* &lt;math&gt;\phi(x)\ge0&lt;/math&gt; is a nonnegative configuration-space field.

An example seed-field construction is:

&lt;math&gt;
\phi(x)=\sum_k \exp\!\left(-\frac{\|x-s_k\|^2}{2\sigma^2}\right)
&lt;/math&gt;

where &lt;math&gt;s_k&lt;/math&gt; are seed locations and &lt;math&gt;\sigma&lt;/math&gt; controls the width of the seed influence.

The two-point correlation function may be estimated using the normalized Landy–Szalay estimator:

&lt;math&gt;
\xi(r)
=
\frac{DD(r)-2DR(r)+RR(r)}{RR(r)}
&lt;/math&gt;

where &lt;math&gt;DD&lt;/math&gt;, &lt;math&gt;DR&lt;/math&gt;, and &lt;math&gt;RR&lt;/math&gt; are normalized pair counts.

{{Note|Unless observational datasets are explicitly supplied, demonstrations may use synthetic target correlation curves for methodological illustration only. Synthetic demonstrations should not be interpreted as empirical cosmological evidence.}}

When run using synthetic target curves, PDT-resampled catalogs may exhibit enhanced small-scale clustering relative to the baseline configuration.

=== Computational demonstrations ===

Reference implementations and supplementary simulation notebooks may be maintained on external repositories or supplementary Wikiversity pages.

{{collapse top|Python demonstration placeholder}}

&lt;syntaxhighlight lang=&quot;python&quot;&gt;
# Example implementations may be maintained separately
# on GitHub, OSF, or supplementary Wikiversity pages.
&lt;/syntaxhighlight&gt;

{{collapse bottom}}


== Scope and Limitations ==

PDT is a mathematical framework for measure transformations. It does not claim:

* a replacement theory for General Relativity or Quantum Mechanics;
* empirical confirmation without explicit predictions and tests;
* observational validation without independently reproducible analysis.

The following discussion extends beyond the primary mathematical framework developed earlier in the article and explores possible conceptual implications and speculative generalizations.

== Speculative Extensions and Geometric Renormalization ==

''This section is speculative and exploratory in nature.''

Recent mathematical work published in the ''Journal of Applied Probability'' by Baryshnikov, Cao, Kahle, and Liu suggests a possible connection between probability distributions and intrinsic geometry.

Studies of “Buffon deficits” on curved manifolds indicate that deviations from classical flat-space Buffon probabilities may encode curvature-dependent geometric information. Within the PDT framework, these observations motivate the broader possibility that geometric structure may influence iterative probabilistic dynamics through curvature-dependent statistical weighting effects.
Within PDT, these results are conceptually relevant because they suggest that probabilistic weighting structures may encode nontrivial geometric information. In particular, the Cambridge analysis demonstrates that generalized Buffon-type probabilistic constructions can reflect Gaussian curvature in different geometries. PDT extends this probabilistic perspective by exploring how iterative probability-measure transformations under positive dilation fields may generate evolving statistical structure, entropy flow, and geometry-dependent probabilistic behavior under repeated transformation.
At present these ideas remain exploratory and heuristic. No direct physical interpretation is presently established within the PDT framework. Within the PDT framework, this motivates the speculative possibility that curvature could act as a statistical weighting mechanism on classes of admissible paths or configurations.

== Future directions ==

* develop canonical families of dilation fields and invariants;
* clarify “structure-from-measure” diagnostics;
* publish reproducible simulation notebooks and parameter sweeps;
* compare multiple dilation families under shared evaluation criteria;
* investigate connections between probabilistic geometry and curvature-dependent statistical measures.
== Future Directions: Probability Element (PE) ==

A speculative extension of Probability Dilation Theory (PDT) is the introduction of a minimal invariant scale in probability-state space, referred to as a '''Probability Element (PE)'''. This concept lies outside standard Fisher information geometry and is not part of established physics.

The PE hypothesis proposes that probability-state space may not be fully continuous, but may instead admit a smallest distinguishable scale of structure in terms of information-theoretic resolution.

This can be expressed in terms of a dimensionless ratio:

&lt;math&gt;\eta = \frac{\sigma_P}{\sigma}&lt;/math&gt;

where:

&lt;math&gt;\sigma_P&lt;/math&gt; is a hypothesized minimal probability-resolution scale,
&lt;math&gt;\sigma&lt;/math&gt; is an effective distinguishability scale in probability-state space.

=== Conceptual motivation ===

Standard Fisher information geometry treats probability distributions as points on a smooth manifold with arbitrarily fine distinguishability. The PE hypothesis explores the possibility that this distinguishability may have a lower bound, introducing a form of discreteness in probability-state geometry.

=== Illustrative toy model (not derived physics) ===

As a heuristic example, one may consider a modification to special relativistic time dilation of the form:

&lt;math&gt;d\tau = dt\sqrt{1 - \frac{v^2}{c^2}}\sqrt{1 - \eta^2}&lt;/math&gt;

where:

&lt;math&gt;v&lt;/math&gt; is velocity,
&lt;math&gt;c&lt;/math&gt; is the speed of light,
&lt;math&gt;\eta = \sigma_P / \sigma&lt;/math&gt; encodes a proposed probability-resolution scale.

This expression is constructed such that standard special relativity is recovered exactly in the limit &lt;math&gt;\eta \to 0&lt;/math&gt;.

=== Status ===

The Probability Element concept is:

Not part of standard Fisher information geometry
not derived from quantum mechanics or general relativity
not currently empirically established.

It is included only as a speculative direction for exploring whether probability-state space admits a minimal geometric resolution scale.

=== Open questions ===

Key open research directions include:

Whether a consistent discrete formulation of probability geometry can be constructed.

Whether a fundamental probability-resolution scale &lt;math&gt;\sigma_P&lt;/math&gt; can be derived from known physical principles.

Whether such a structure could lead to measurable deviations from standard statistical or relativistic predictions.

== Convergence behavior ==

Iterative PDT transformations may exhibit qualitatively different convergence behavior depending on the structure of the applied dilation field. Repeated probabilistic reweighting can produce entropy reduction, probability concentration, oscillatory behavior, or fluctuating stochastic dynamics over successive iterations.

=== Qualitative convergence classes ===

Exploratory finite-state PDT experiments suggest several broad classes of iterative behavior:

* '''Concentrating regimes''' — repeated transformations progressively concentrate probability mass into localized regions, often accompanied by decreasing Shannon entropy.

* '''Oscillatory regimes''' — probability structure evolves through recurring redistribution patterns without strong long-term concentration.

* '''Multi-peak regimes''' — multiple semi-stable concentration regions emerge simultaneously, producing persistent structured probability distributions.

* '''Stochastic regimes''' — fluctuating probabilistic structure evolves under partially random or time-dependent weighting behavior.

=== Entropy and convergence ===

In many exploratory PDT experiments, entropy reduction correlates with increasing probability concentration under repeated transformation. However, some oscillatory and stochastic field classes may preserve higher entropy distributions or exhibit fluctuating convergence behavior over time.

The relationship between entropy evolution and convergence remains an open area of investigation. Future work may examine entropy rates, stability properties, and long-term probabilistic structure under repeated PDT transformations.

=== Attractor-like behavior ===

Some iterative PDT systems may exhibit transient attractor-like probabilistic structure in finite-state computational experiments. These behaviors are presently exploratory and are not established mathematical attractors in the formal dynamical-systems sense.

Future investigation of PDT convergence behavior may include stability analysis, fixed-point structure, stochastic convergence properties, and comparison with established dynamical systems and probabilistic evolution frameworks.

== Current limitations ==
PDT presently operates as an exploratory probabilistic and computational framework. The theory does not presently derive known physical laws from first principles, nor does it replace established formulations of quantum mechanics or general relativity. Current PDT investigations primarily focus on iterative probability transformations, entropy evolution, probabilistic weighting behavior, and computationally modeled structure formation.
Many proposed physical interpretations associated with PDT remain speculative and exploratory. Existing computational experiments are finite-state toy models intended to illustrate qualitative probabilistic behavior rather than experimentally verified physical mechanisms.
Future development of PDT would likely require additional mathematical formalization, convergence analysis, stochastic modeling, and comparison with established probabilistic and dynamical systems frameworks.

== See also ==

* [[w:Buffon's needle problem|Buffon's needle problem]]
* [[w:Probability measure|Probability measure]]
* [[w:Importance sampling|Importance sampling]]
* [[w:Radon–Nikodym theorem|Radon–Nikodym theorem]]
* [[w:Dynamical system|Dynamical systems]]

* [[w:Entropy (information theory)|Entropy]]
* [[w:Information theory|Information theory]]
* [[w:Measure theory|Measure theory]]
* [[w:Geometric probability|Geometric probability]]

* [[w:Shannon entropy|Shannon entropy]]
* [[w:Stochastic process|Stochastic process]]
* [[w:Fixed point (mathematics)|Fixed point]]
* [[w:Convergence (mathematics)|Convergence]]

== Related probabilistic and geometric literature ==

Related literature on probabilistic dilation, conditioning behavior, geometric probability, and curvature-dependent probabilistic structure includes the following works:

* Augustin, T.; Coolen, F. P. A.; de Cooman, G.; Troffaes, M. C. M. ''Introduction to Imprecise Probabilities''. Wiley, 2014.

* Baryshnikov, Y.; Cao, Y.; Kahle, M.; Liu, J. (2024). ''Buffon’s problem on curved surfaces and Gaussian curvature''. ''Journal of Applied Probability''. Cambridge University Press. doi:10.1017/jpr.2024.19

* Herron, T.; Seidenfeld, T.; Wasserman, L. ''Divisive Conditioning: Further Results on Dilation''. Philosophy of Science, Vol. 64, No. 3, 1997.

* Herron, T.; Seidenfeld, T.; Wasserman, L. ''Distention for Sets of Probabilities''. Annals of Mathematics and Artificial Intelligence, Vol. 45, 2005.

* Moral, S.; Wilson, N. ''Dilation Properties of Coherent Nearly-Linear Models''. International Journal of Approximate Reasoning, Vol. 45, 2007.

* Shannon, C. E. (1948). ''A Mathematical Theory of Communication''. ''Bell System Technical Journal'', 27(3), 379–423; 27(4), 623–656.

== Copyright and licensing ==

Text and original figures © Howard Richardson.

Licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Reuse permitted with attribution.</text>
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{{Original research}}
{{To be peer reviewed}}


== Research abstract ==
'''Probability Dilation Theory (PDT)''' is a measure-theoretic research framework for studying how probability measures transform under '''positive reweighting (dilation)''' while preserving normalization and producing controlled changes in expectation values.

The theory is an exploratory framework for iterative probability-measure evolution under positive dilation fields. The framework studies how repeated probabilistic reweighting transformations may generate emergent statistical structure, entropy flow, and multiscale probability dynamics.

At its core, PDT studies how repeated positive probability reweighting transformations alter the long-term structure of probability distributions.
PDT treats a probability measure as the primary mathematical object and investigates:
* invariant identities induced by reweighting,
* composition and iteration of dilations,
* fixed points and near-fixed behavior,
* whether iterative measure updates can generate testable multiscale statistical structure (to be evaluated via explicit models and simulations).

PDT is presented as a mathematical framework. Any proposed application to physics or cosmology must be expressed as a concrete model (space, baseline measure, dilation field) and tested against falsifiable predictions.

== Overview ==
PDT is motivated by the observation that some structural information can be recovered from sampling statistics (e.g., [[w:Buffon's needle problem|Buffon’s needle]]). PDT abstracts this idea by focusing on measure transformation itself: a dilation field modifies a baseline probability measure in a way that is:
* mathematically well-defined (positivity and normalization),
* composable under iteration,
* analyzable for invariants and fixed points.
=== Conceptual interpretation ===

A simplified conceptual flow of the PDT framework is:

&lt;pre&gt;
Baseline probability measure P
            ↓
Positive dilation field D(x)
            ↓
Reweighted probability measure P~
            ↓
Observable statistical changes
&lt;/pre&gt;
Repeated dilation may qualitatively behave as:

&lt;pre&gt;
Broad initial distribution
        ↓
Localized reweighting
        ↓
Probability concentration
        ↓
Emergent multiscale structure
&lt;/pre&gt;

Different classes of dilation fields may therefore generate qualitatively different long-term probability dynamics.
In this interpretation, PDT does not alter the underlying sample space directly. Instead, it modifies how probability mass is distributed across that space through a positive reweighting field.

Regions with larger values of the dilation field contribute more strongly to the transformed measure, while normalization preserves total probability. Earlier exploratory formulations of Probability Dilation Theory (PDT) were informally referred to as the Einstein Buffon Process (EBP), reflecting initial probabilistic-geometric interpretations inspired by Buffon-type constructions and Einstein-style scaling analogies. The framework has since evolved toward a broader iterative theory of probability-measure dynamics under positive dilation fields. A simple iterative interpretation may also be visualized as:

&lt;pre&gt;
P₀
 ↓ D₁
P₁
 ↓ D₂
P₂
 ↓ D₃
P₃
 ↓ ⋯
&lt;/pre&gt;

where each dilation field reweights the probability structure generated by the previous step.

Different classes of dilation fields may therefore generate qualitatively different long-term probability dynamics.

= Mathematical framework =

== Definitions and notation ==
Let &lt;math&gt;(\Omega,\Sigma)&lt;/math&gt; be a measurable space.

* &lt;math&gt;P&lt;/math&gt; denotes a probability measure on &lt;math&gt;(\Omega,\Sigma)&lt;/math&gt;.
* If &lt;math&gt;P&lt;/math&gt; has a density &lt;math&gt;p&lt;/math&gt; with respect to a reference measure &lt;math&gt;\mu&lt;/math&gt;, then &lt;math&gt;dP=p\,d\mu&lt;/math&gt;.
* &lt;math&gt;D:\Omega\to(0,\infty)&lt;/math&gt; is a measurable '''dilation field''' (a positive weight function).
* &lt;math&gt;Z(P,D)&lt;/math&gt; is the normalization constant:
.&lt;math&gt;
Z(P,D)=\int_\Omega D\,dP
&lt;/math&gt;
* For an observable &lt;math&gt;f:\Omega\to\mathbb{R}&lt;/math&gt; integrable under the relevant measure,
&lt;math&gt;
\mathbb{E}_P[f]
=
\int_\Omega f\,dP
&lt;/math&gt;.

== PDT transformation (probability reweighting) ==

Given &lt;math&gt;P&lt;/math&gt; and &lt;math&gt;D&lt;/math&gt; with &lt;math&gt;0&lt;Z(P,D)&lt;\infty&lt;/math&gt;, define the '''PDT transform''' &lt;math&gt;\widetilde{P}=\mathrm{PDT}(P;D)&lt;/math&gt; by:

&lt;math&gt;
\widetilde{P}(A)
=
\frac{
\int_A D\,dP
}{
\int_\Omega D\,dP
}
\quad\text{for all }A\in\Sigma
&lt;/math&gt;

If &lt;math&gt;dP=p\,d\mu&lt;/math&gt;, then &lt;math&gt;d\widetilde{P}=\widetilde{p}\,d\mu&lt;/math&gt;, where

&lt;math&gt;
\widetilde{p}(x)
=
\frac{D(x)\,p(x)}{Z}
&lt;/math&gt;

and

&lt;math&gt;
Z
=
\int_\Omega D(x)\,p(x)\,d\mu
&lt;/math&gt;

'''Interpretation:''' the dilation field &lt;math&gt;D&lt;/math&gt; shifts probability mass toward regions where &lt;math&gt;D&lt;/math&gt; is larger, while renormalization keeps total probability equal to 1.

PDT is mathematically related to importance sampling, Gibbs-style reweighting, and Radon–Nikodym measure transformations, although the framework emphasizes compositional and geometric interpretations of probability reweighting rather than only numerical estimation procedures.

Unlike conventional importance sampling, however, PDT emphasizes the compositional and potentially dynamical behavior of repeated probability reweighting transformations.
A familiar physical example of a strictly positive factor is the Lorentz factor:

&lt;math&gt;
\gamma(v)
=
\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}
&lt;/math&gt;

for

&lt;math&gt;
|v|&lt;c
&lt;/math&gt;

Lorentz contraction for a rod of rest length &lt;math&gt;L_0&lt;/math&gt; moving at speed &lt;math&gt;v&lt;/math&gt; is:

&lt;math&gt;
L(v)=\frac{L_0}{\gamma(v)}
&lt;/math&gt;

To connect this idea to PDT (as an illustration only), one may define a positive dilation field based on &lt;math&gt;\gamma&lt;/math&gt;.

== Worked finite example ==

Consider a finite probability space:

&lt;math&gt;
\Omega=\{a,b,c\}
&lt;/math&gt;

with baseline probabilities:

&lt;math&gt;
P(a)=0.2,\quad
P(b)=0.3,\quad
P(c)=0.5
&lt;/math&gt;

Define a positive dilation field:

&lt;math&gt;
D(a)=1,\quad
D(b)=2,\quad
D(c)=4
&lt;/math&gt;

The normalization constant is:

&lt;math&gt;
Z=\sum_x D(x)P(x)
&lt;/math&gt;

giving:

&lt;math&gt;
Z=(1)(0.2)+(2)(0.3)+(4)(0.5)=2.8
&lt;/math&gt;

The PDT-transformed probabilities become:

&lt;math&gt;
\widetilde{P}(a)=\frac{0.2}{2.8}\approx0.071
&lt;/math&gt;

&lt;math&gt;
\widetilde{P}(b)=\frac{0.6}{2.8}\approx0.214
&lt;/math&gt;

&lt;math&gt;
\widetilde{P}(c)=\frac{2.0}{2.8}\approx0.714
&lt;/math&gt;

This illustrates how PDT shifts probability mass toward regions with larger dilation weights while preserving normalization.

== Composition of dilations ==

An important structural property of sequential PDT transformations is that compose multiplicatively.

Suppose two positive dilation fields:

&lt;math&gt;
D_1(x)&gt;0
&lt;/math&gt;

and

&lt;math&gt;
D_2(x)&gt;0
&lt;/math&gt;

are applied successively to a baseline probability measure &lt;math&gt;P&lt;/math&gt;.

The first dilation produces:

&lt;math&gt;
\widetilde{P}_1(A)
=
\frac{\int_A D_1\,dP}
{\int_\Omega D_1\,dP}
&lt;/math&gt;

Applying the second dilation field to &lt;math&gt;\widetilde{P}_1&lt;/math&gt; gives:

&lt;math&gt;
\widetilde{P}_2(A)
=
\frac{\int_A D_2\,d\widetilde{P}_1}
{\int_\Omega D_2\,d\widetilde{P}_1}
&lt;/math&gt;

Substituting the first transformation into the second yields:

&lt;math&gt;
\widetilde{P}_2(A)
=
\frac{
\int_A D_2D_1\,dP
}{
\int_\Omega D_2D_1\,dP
}
&lt;/math&gt;

This shows that sequential PDT transformations compose through multiplication of the dilation fields.

This compositional structure allows iterative probability reweighting to be studied using products of positive fields, potentially generating multiscale or hierarchical probability structures under repeated application.

== Fixed points and iterative dynamics ==

An important question in PDT concerns the long-term behavior of repeated PDT transformations.

Given an initial probability measure:

&lt;math&gt;
P_0
&lt;/math&gt;

and a sequence of positive dilation fields:

&lt;math&gt;
D_1,D_2,D_3,\dots
&lt;/math&gt;

successive PDT transformations generate a sequence of measures:

&lt;math&gt;
P_0
\rightarrow
P_1
\rightarrow
P_2
\rightarrow
P_3
\rightarrow \cdots
&lt;/math&gt;

where each transformed measure is obtained by reweighting the previous one.

A measure &lt;math&gt;P&lt;/math&gt; is called a fixed point of a dilation field &lt;math&gt;D&lt;/math&gt; if:

&lt;math&gt;
\widetilde{P}=P
&lt;/math&gt;

under the PDT transformation.

In the simplest case, this requires the dilation field to be constant almost everywhere with respect to &lt;math&gt;P&lt;/math&gt;. More general fixed-point behavior may arise when iterative compositions balance probability amplification against normalization.

More generally, repeated compositions of nontrivial dilation fields may generate:

* hierarchical probability structure;
* multiscale statistical behavior;
* attractor-like distributions;
* approximately stable transformed measures.

These questions connect PDT to broader areas of:

* dynamical systems;
* stochastic processes;
* iterative renormalization methods;
* probabilistic geometry.

At present these iterative properties remain largely unexplored within the PDT framework.

== Entropy and iterative probability flow ==

Repeated PDT transformations may alter the entropy structure of a probability measure.

For a discrete probability distribution:

&lt;math&gt;
P=\{p_i\}
&lt;/math&gt;

the Shannon entropy is:

&lt;math&gt;
H(P)
=
-\sum_i p_i \log p_i
&lt;/math&gt;

Under iterative PDT transformation, successive transformed measures:

&lt;math&gt;
P_0
\rightarrow
P_1
\rightarrow
P_2
\rightarrow \cdots
&lt;/math&gt;

may exhibit changing entropy behavior depending on the structure of the dilation fields.

For example:
* strongly localized dilation fields may concentrate probability mass and reduce entropy;
* broader or smoothing dilation fields may distribute probability more evenly and increase entropy;
* iterative compositions may generate approximately stable entropy profiles.

These questions connect PDT to:
* information theory,
* statistical mechanics,
* stochastic dynamics,
* and renormalization-style iterative systems.

At present the entropy behavior of iterative PDT transformations remains an open area for investigation.

== Toy experiment: entropy under repeated dilation ==

A simple finite-state experiment illustrates how repeated PDT transformations can change the entropy of a probability distribution.

Let the initial probability distribution be:

&lt;math&gt;
P_0=(0.2,0.2,0.2,0.2,0.2)
&lt;/math&gt;

and define a positive dilation field:

&lt;math&gt;
D=(1,1,2,4,8)
&lt;/math&gt;

At each step, apply the PDT update:

&lt;math&gt;
P_{n+1}(i)
=
\frac{D(i)P_n(i)}
{\sum_j D(j)P_n(j)}
&lt;/math&gt;

The Shannon entropy is:

&lt;math&gt;
H(P_n)
=
-\sum_i P_n(i)\log P_n(i)
&lt;/math&gt;

In this toy model, repeated dilation shifts probability mass toward the highest-weight state. Over ten iterations, the entropy decreases from approximately:

&lt;math&gt;
H(P_0)\approx1.6094
&lt;/math&gt;

to:

&lt;math&gt;
H(P_{10})\approx0.00775
&lt;/math&gt;

The final distribution is approximately:

&lt;math&gt;
P_{10}
\approx
(0.000000001,\;0.000000001,\;0.000000953,\;0.000975609,\;0.999023437)
&lt;/math&gt;

This example demonstrates probability concentration under repeated positive dilation. It is a finite-state toy model and should not be interpreted as physical evidence; its purpose is to illustrate iterative PDT behavior.
== Mathematical context ==
PDT transformations may be viewed as exploratory probability-measure reweighting procedures related conceptually to conditioning behavior, stochastic transformations, entropy evolution, and probabilistic dilation phenomena studied in imprecise probability theory and dynamical systems literature.
In PDT, the term ''dilation'' refers to probabilistic reweighting and transformation behavior under localized weighting fields rather than the formal operator-theoretic notion of dilation used in functional analysis.
The iterative entropy-flow experiments explored in PDT resemble finite-state dynamical systems in which repeated transformations generate convergence, concentration, and emergent probabilistic structure over successive iterations.
=== Example entropy evolution ===

{| class=&quot;wikitable&quot;
! Iteration !! Shannon entropy
|-
| 0 || 1.6094
|-
| 1 || 1.2990
|-
| 2 || 0.7790
|-
| 3 || 0.4399
|-
| 5 || 0.1500
|-
| 10 || 0.0078
|}
Entropy evolution under repeated localized PDT transformation showing entropy reduction and probability concentration under iterative probabilistic reweighting. Programmatically generated using Python in a ChatGPT-assisted workflow. The entropy decreases under repeated application of the dilation field as probability mass becomes increasingly concentrated in the highest-weight states.
=== Localized dilation fields ===

A useful class of PDT transformations is generated by localized positive dilation fields.

Consider a one-dimensional finite configuration space with states indexed by:

&lt;math&gt;
x=0,1,2,\dots,N
&lt;/math&gt;

and define a localized dilation field centered at &lt;math&gt;x_0&lt;/math&gt;:

&lt;math&gt;
D(x)
=
\exp\!\left(
\lambda
\exp\!\left(
-\frac{(x-x_0)^2}{2\sigma^2}
\right)
\right)
&lt;/math&gt;

where:

* &lt;math&gt;\lambda&gt;0&lt;/math&gt; controls the strength of the dilation;
* &lt;math&gt;\sigma&lt;/math&gt; controls the spatial width of the localized field.

Narrow values of &lt;math&gt;\sigma&lt;/math&gt; produce sharply localized amplification, while broader values produce smoother probability reweighting across the configuration space.

Under iterative PDT dynamics:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D(x)P_n(x)
}{
\sum_y D(y)P_n(y)
}
&lt;/math&gt;

the probability distribution may progressively concentrate near the center of the dilation field.

=== Example entropy evolution for localized fields ===

Using an initially uniform distribution over 21 states and iterating the PDT transformation 10 times produces the following representative entropy behavior:

{| class=&quot;wikitable&quot;
! Field width &lt;math&gt;\sigma&lt;/math&gt;
! Final entropy after 10 iterations
! Maximum probability after 10 iterations
|-
| 1.5 || 0.0352 || 0.9950
|-
| 3.0 || 0.8162 || 0.7141
|-
| 6.0 || 1.5367 || 0.3595
|}
[[File:PDT entropy evolution localized field.png|thumb|center|600px|Entropy evolution under repeated localized PDT transformation showing entropy reduction and probability concentration under iterative probabilistic reweighting.]]
[[File:Epd_entropy_evolution.png|thumb|center|600px|Entropy evolution under repeated localized PDT dilation. Narrow localized dilation fields produce rapid entropy reduction and probability concentration under iterative reweighting.]]
These results indicate that narrower localized dilation fields generate stronger probability concentration and more rapid entropy reduction.

== Comparative entropy-flow experiments ==

The following finite-state computational experiments illustrate comparative entropy evolution under several classes of PDT dilation fields. Each experiment begins with the same initially uniform probability distribution and applies repeated PDT transformations under different field structures. The experiments are exploratory and intended to illustrate qualitative differences in iterative probabilistic behavior rather than empirical physical predictions.
{| class=&quot;wikitable&quot;
|+ Comparative entropy-flow behavior under PDT field classes
! Field class
! Final entropy
! Entropy decrease
! Final max probability
! Qualitative behavior
|-
| Localized
| 0.3104
| 3.4032
| 0.9275
| Strong probability concentration
|-
| Oscillatory
| 1.5779
| 2.1357
| 0.3418
| Distributed oscillatory structure
|-
| Multi-peak
| 0.2851
| 3.4284
| 0.9425
| Multiple concentration regions
|-
| Stochastic
| 0.7744
| 2.9392
| 0.7413
| Fluctuating concentration behavior
|}
These experiments suggest that different classes of dilation fields may generate qualitatively distinct entropy-flow and concentration behavior under iterative PDT dynamics. Localized and multi-peak fields produce strong entropy reduction and probability concentration, while oscillatory fields preserve more distributed probabilistic structure. Stochastic fields exhibit fluctuating but still partially concentrating behavior in this finite-state example.
In this toy model, repeated localized dilation behaves qualitatively like an attractor centered on the highest-weight region of the configuration space.
[[File:Pdt comparative entropy flow.png|thumb|Comparative entropy evolution under localized, oscillatory, multi-peak, and stochastic PDT dilation fields.]]
The experiment is intended only as a finite-state demonstration of iterative PDT dynamics and should not be interpreted as physical evidence.

=== Oscillatory dilation fields ===

Another useful class of PDT transformations is generated by oscillatory positive dilation fields.

One example is:

&lt;math&gt;
D(x)
=
\exp(\lambda\sin(kx))
&lt;/math&gt;

where:

* &lt;math&gt;\lambda&gt;0&lt;/math&gt; controls the strength of the oscillatory amplification;
* &lt;math&gt;k&lt;/math&gt; controls the spatial frequency of the oscillation.

Because the exponential is always positive, the dilation field remains strictly positive for all states.

Unlike localized dilation fields, oscillatory fields may generate multiple competing high-weight regions across the configuration space.

Under repeated PDT transformation:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D(x)P_n(x)
}{
\sum_y D(y)P_n(y)
}
&lt;/math&gt;

probability mass may evolve toward several distributed concentration regions rather than a single dominant attractor.

=== Example oscillatory-field experiment ===

A finite-state experiment was performed using:

* 41 discrete states;
* an initially uniform probability distribution;
* a positive oscillatory dilation field with three spatial oscillation cycles;
* 10 successive PDT iterations.

Representative entropy behavior was:

{| class=&quot;wikitable&quot;
! Iteration
! Shannon entropy
|-
| 0 || 3.7136
|-
| 2 || 2.8699
|-
| 5 || 2.3018
|-
| 10 || 1.9335
|}

Unlike sharply localized dilation fields, the oscillatory field produced slower entropy reduction and multiple probability concentration peaks distributed across the configuration space.

After 10 iterations, the largest probability concentration remained distributed rather than collapsing into a single dominant state.

This suggests that different classes of positive dilation fields may generate qualitatively different long-term iterative probability structures.

The experiment is intended only as a finite-state demonstration of iterative PDT dynamics and should not be interpreted as physical evidence.
=== Multi-peak localized dilation fields ===

A broader class of PDT transformations may be generated using multiple localized dilation peaks distributed across the configuration space.

One example is:

&lt;math&gt;
D(x)
=
\exp\!\left(
\sum_k
\lambda_k
\exp\!\left(
-\frac{(x-x_k)^2}{2\sigma_k^2}
\right)
\right)
&lt;/math&gt;

where:

* &lt;math&gt;x_k&lt;/math&gt; are the locations of the dilation peaks;
* &lt;math&gt;\lambda_k&gt;0&lt;/math&gt; control the amplification strength of each peak;
* &lt;math&gt;\sigma_k&lt;/math&gt; control the spatial width of each localized region.

This construction generates a positive multimodal dilation landscape containing several competing amplification regions.

Under repeated PDT iteration:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D(x)P_n(x)
}{
\sum_y D(y)P_n(y)
}
&lt;/math&gt;

probability mass may evolve toward multiple partially localized concentration regions.

Unlike single localized dilation fields, multi-peak fields may generate:

* competing attractor-like regions;
* hierarchical probability concentration;
* partially stabilized multimodal distributions;
* multiscale probability structure.

Depending on the relative strengths and widths of the peaks, the iterative dynamics may favor:
* dominance by a single peak;
* coexistence of several concentration regions;
* or slowly evolving metastable probability structures.

=== Conceptual interpretation ===

A qualitative iterative evolution may be visualized as:

&lt;pre&gt;
Broad initial distribution
        ↓
Multiple localized amplifications
        ↓
Competing concentration regions
        ↓
Emergent multimodal probability structure
&lt;/pre&gt;

This class of dilation fields suggests that iterative PDT dynamics may generate richer probability organization than either single localized attractors or simple oscillatory fields alone.

At present these behaviors remain exploratory computational observations within finite-state toy models.
=== Random and stochastic dilation fields ===

Another important class of PDT transformations arises when the dilation field itself varies stochastically.

A simple stochastic dilation field may be written schematically as:

&lt;math&gt;
D_n(x)
=
\exp\!\left(
\sigma \eta_n(x)
\right)
&lt;/math&gt;

where:

* &lt;math&gt;\eta_n(x)&lt;/math&gt; is a random field or stochastic fluctuation at iteration &lt;math&gt;n&lt;/math&gt;;
* &lt;math&gt;\sigma&gt;0&lt;/math&gt; controls the strength of the stochastic variation.

Because the exponential is strictly positive, the dilation field remains positive for all realizations of the random process.

Under repeated PDT iteration:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D_n(x)P_n(x)
}{
\sum_y D_n(y)P_n(y)
}
&lt;/math&gt;

the probability landscape itself fluctuates dynamically from one iteration to the next.

Unlike deterministic localized or oscillatory dilation fields, stochastic dilation fields may generate:

* fluctuating concentration regions;
* transient attractor-like structures;
* noise-driven entropy evolution;
* intermittent probability concentration;
* metastable probabilistic configurations.

=== Conceptual interpretation ===

A qualitative stochastic evolution may be visualized as:

&lt;pre&gt;
Broad initial distribution
        ↓
Random localized amplification
        ↓
Fluctuating concentration regions
        ↓
Dynamic probabilistic structure
&lt;/pre&gt;

Depending on the stochastic process used to generate the dilation fields, the long-term dynamics may exhibit:
* partial concentration,
* persistent fluctuations,
* stochastic stabilization,
* or continuously evolving probabilistic structure.

These ideas connect PDT to broader areas of:
* stochastic processes;
* random multiplicative systems;
* statistical mechanics;
* noise-driven dynamical systems;
* probabilistic geometry.

At present these behaviors remain exploratory computational possibilities within finite-state toy models.

== Qualitative classes of iterative PDT behavior ==

Different classes of positive dilation fields may generate qualitatively different long-term probability dynamics under repeated PDT transformation.

The following table summarizes several representative classes explored within finite-state toy models.

{| class=&quot;wikitable&quot;
! Dilation-field class
! Typical iterative behavior
! Representative qualitative structure
|-
| Localized fields
| Strong entropy reduction and concentration toward a dominant region
| Single attractor-like concentration
|-
| Oscillatory fields
| Distributed amplification with slower entropy reduction
| Patterned multimodal structure
|-
| Multi-peak localized fields
| Competition between several concentration regions
| Hierarchical or metastable probability structure
|-
| Random and stochastic fields
| Fluctuating amplification and noise-driven evolution
| Dynamic probabilistic landscapes
|}

These examples suggest that iterative PDT reweighting may generate a broad spectrum of emergent statistical structures depending on the geometry and dynamics of the dilation field.

Within the PDT framework, the iterative behavior of probability measures may therefore depend as strongly on the structure of the dilation field as on the initial probability distribution itself.

At present these qualitative behaviors remain exploratory computational observations within finite-state toy models.

== Numerical simulation and iterative models ==

=== Simulation model description ===

In discrete demonstrations, the “state space” may be represented by a finite set such as bins, configurations, or catalog points.

Two equivalent discrete implementations are common:

* '''weighted evaluation''': retain all points and assign weights proportional to &lt;math&gt;D&lt;/math&gt;;
* '''importance resampling''': generate a new empirical catalog with sampling probabilities proportional to &lt;math&gt;D&lt;/math&gt;.

=== Demonstration: reweighting mock galaxy catalogs ===

A simple computational demonstration of PDT may be constructed using synthetic galaxy catalogs in a periodic simulation box.

The demonstration pipeline is:

# generate a baseline mock catalog;
# define a positive dilation field over the configuration space;
# perform PDT-style importance resampling;
# compute the resulting two-point correlation function &lt;math&gt;\xi(r)&lt;/math&gt;;
# compare transformed and baseline catalogs.

One example dilation field is:

&lt;math&gt;
D(x)=\exp(\lambda\phi(x))
&lt;/math&gt;

where:

* &lt;math&gt;\lambda&gt;0&lt;/math&gt; controls the strength of the dilation;
* &lt;math&gt;\phi(x)\ge0&lt;/math&gt; is a nonnegative configuration-space field.

An example seed-field construction is:

&lt;math&gt;
\phi(x)=\sum_k \exp\!\left(-\frac{\|x-s_k\|^2}{2\sigma^2}\right)
&lt;/math&gt;

where &lt;math&gt;s_k&lt;/math&gt; are seed locations and &lt;math&gt;\sigma&lt;/math&gt; controls the width of the seed influence.

The two-point correlation function may be estimated using the normalized Landy–Szalay estimator:

&lt;math&gt;
\xi(r)
=
\frac{DD(r)-2DR(r)+RR(r)}{RR(r)}
&lt;/math&gt;

where &lt;math&gt;DD&lt;/math&gt;, &lt;math&gt;DR&lt;/math&gt;, and &lt;math&gt;RR&lt;/math&gt; are normalized pair counts.

{{Note|Unless observational datasets are explicitly supplied, demonstrations may use synthetic target correlation curves for methodological illustration only. Synthetic demonstrations should not be interpreted as empirical cosmological evidence.}}

When run using synthetic target curves, PDT-resampled catalogs may exhibit enhanced small-scale clustering relative to the baseline configuration.

=== Computational demonstrations ===

Reference implementations and supplementary simulation notebooks may be maintained on external repositories or supplementary Wikiversity pages.

{{collapse top|Python demonstration placeholder}}

&lt;syntaxhighlight lang=&quot;python&quot;&gt;
# Example implementations may be maintained separately
# on GitHub, OSF, or supplementary Wikiversity pages.
&lt;/syntaxhighlight&gt;

{{collapse bottom}}


== Scope and Limitations ==

PDT is a mathematical framework for measure transformations. It does not claim:

* a replacement theory for General Relativity or Quantum Mechanics;
* empirical confirmation without explicit predictions and tests;
* observational validation without independently reproducible analysis.

The following discussion extends beyond the primary mathematical framework developed earlier in the article and explores possible conceptual implications and speculative generalizations.

== Speculative Extensions and Geometric Renormalization ==

''This section is speculative and exploratory in nature.''

Recent mathematical work published in the ''Journal of Applied Probability'' by Baryshnikov, Cao, Kahle, and Liu suggests a possible connection between probability distributions and intrinsic geometry.

Studies of “Buffon deficits” on curved manifolds indicate that deviations from classical flat-space Buffon probabilities may encode curvature-dependent geometric information. Within the PDT framework, these observations motivate the broader possibility that geometric structure may influence iterative probabilistic dynamics through curvature-dependent statistical weighting effects.
Within PDT, these results are conceptually relevant because they suggest that probabilistic weighting structures may encode nontrivial geometric information. In particular, the Cambridge analysis demonstrates that generalized Buffon-type probabilistic constructions can reflect Gaussian curvature in different geometries. PDT extends this probabilistic perspective by exploring how iterative probability-measure transformations under positive dilation fields may generate evolving statistical structure, entropy flow, and geometry-dependent probabilistic behavior under repeated transformation.
At present these ideas remain exploratory and heuristic. No direct physical interpretation is presently established within the PDT framework. Within the PDT framework, this motivates the speculative possibility that curvature could act as a statistical weighting mechanism on classes of admissible paths or configurations.

== Future directions ==

* develop canonical families of dilation fields and invariants;
* clarify “structure-from-measure” diagnostics;
* publish reproducible simulation notebooks and parameter sweeps;
* compare multiple dilation families under shared evaluation criteria;
* investigate connections between probabilistic geometry and curvature-dependent statistical measures.
== Future Directions: Probability Element (PE) ==

A speculative extension of Probability Dilation Theory (PDT) is the introduction of a minimal invariant scale in probability-state space, referred to as a '''Probability Element (PE)'''. This concept lies outside standard Fisher information geometry and is not part of established physics.

The PE hypothesis proposes that probability-state space may not be fully continuous, but may instead admit a smallest distinguishable scale of structure in terms of information-theoretic resolution.

This can be expressed in terms of a dimensionless ratio:

&lt;math&gt;\eta = \frac{\sigma_P}{\sigma}&lt;/math&gt;

where:

&lt;math&gt;\sigma_P&lt;/math&gt; is a hypothesized minimal probability-resolution scale,
&lt;math&gt;\sigma&lt;/math&gt; is an effective distinguishability scale in probability-state space.

=== Conceptual motivation ===

Standard Fisher information geometry treats probability distributions as points on a smooth manifold with arbitrarily fine distinguishability. The PE hypothesis explores the possibility that this distinguishability may have a lower bound, introducing a form of discreteness in probability-state geometry.

=== Illustrative toy model (not derived physics) ===

As a heuristic example, one may consider a modification to special relativistic time dilation of the form:

&lt;math&gt;d\tau = dt\sqrt{1 - \frac{v^2}{c^2}}\sqrt{1 - \eta^2}&lt;/math&gt;

where:

&lt;math&gt;v&lt;/math&gt; is velocity,
&lt;math&gt;c&lt;/math&gt; is the speed of light,
&lt;math&gt;\eta = \sigma_P / \sigma&lt;/math&gt; encodes a proposed probability-resolution scale.

This expression is constructed such that standard special relativity is recovered exactly in the limit &lt;math&gt;\eta \to 0&lt;/math&gt;.

=== Status ===

The Probability Element concept is:

Not part of standard Fisher information geometry
not derived from quantum mechanics or general relativity
not currently empirically established.

It is included only as a speculative direction for exploring whether probability-state space admits a minimal geometric resolution scale.

=== Open questions ===

Key open research directions include:

Whether a consistent discrete formulation of probability geometry can be constructed.

Whether a fundamental probability-resolution scale &lt;math&gt;\sigma_P&lt;/math&gt; can be derived from known physical principles.

Whether such a structure could lead to measurable deviations from standard statistical or relativistic predictions.

== Convergence behavior ==

Iterative PDT transformations may exhibit qualitatively different convergence behavior depending on the structure of the applied dilation field. Repeated probabilistic reweighting can produce entropy reduction, probability concentration, oscillatory behavior, or fluctuating stochastic dynamics over successive iterations.

=== Qualitative convergence classes ===

Exploratory finite-state PDT experiments suggest several broad classes of iterative behavior:

* '''Concentrating regimes''' — repeated transformations progressively concentrate probability mass into localized regions, often accompanied by decreasing Shannon entropy.

* '''Oscillatory regimes''' — probability structure evolves through recurring redistribution patterns without strong long-term concentration.

* '''Multi-peak regimes''' — multiple semi-stable concentration regions emerge simultaneously, producing persistent structured probability distributions.

* '''Stochastic regimes''' — fluctuating probabilistic structure evolves under partially random or time-dependent weighting behavior.

=== Entropy and convergence ===

In many exploratory PDT experiments, entropy reduction correlates with increasing probability concentration under repeated transformation. However, some oscillatory and stochastic field classes may preserve higher entropy distributions or exhibit fluctuating convergence behavior over time.

The relationship between entropy evolution and convergence remains an open area of investigation. Future work may examine entropy rates, stability properties, and long-term probabilistic structure under repeated PDT transformations.

=== Attractor-like behavior ===

Some iterative PDT systems may exhibit transient attractor-like probabilistic structure in finite-state computational experiments. These behaviors are presently exploratory and are not established mathematical attractors in the formal dynamical-systems sense.

Future investigation of PDT convergence behavior may include stability analysis, fixed-point structure, stochastic convergence properties, and comparison with established dynamical systems and probabilistic evolution frameworks.

== Current limitations ==
PDT presently operates as an exploratory probabilistic and computational framework. The theory does not presently derive known physical laws from first principles, nor does it replace established formulations of quantum mechanics or general relativity. Current PDT investigations primarily focus on iterative probability transformations, entropy evolution, probabilistic weighting behavior, and computationally modeled structure formation.
Many proposed physical interpretations associated with PDT remain speculative and exploratory. Existing computational experiments are finite-state toy models intended to illustrate qualitative probabilistic behavior rather than experimentally verified physical mechanisms.
Future development of PDT would likely require additional mathematical formalization, convergence analysis, stochastic modeling, and comparison with established probabilistic and dynamical systems frameworks.

== See also ==

* [[w:Buffon's needle problem|Buffon's needle problem]]
* [[w:Probability measure|Probability measure]]
* [[w:Importance sampling|Importance sampling]]
* [[w:Radon–Nikodym theorem|Radon–Nikodym theorem]]
* [[w:Dynamical system|Dynamical systems]]

* [[w:Entropy (information theory)|Entropy]]
* [[w:Information theory|Information theory]]
* [[w:Measure theory|Measure theory]]
* [[w:Geometric probability|Geometric probability]]

* [[w:Shannon entropy|Shannon entropy]]
* [[w:Stochastic process|Stochastic process]]
* [[w:Fixed point (mathematics)|Fixed point]]
* [[w:Convergence (mathematics)|Convergence]]

== Future research directions ==

Exploratory subpages associated with Probability Dilation Theory (PDT) include:

* [[/Quantum Computing in Dilation Fields|Quantum computing in dilation fields]]
* [[/Fisher Geometry and Dilation Flows|Fisher geometry and dilation flows]]

== Related probabilistic and geometric literature ==

Related literature on probabilistic dilation, conditioning behavior, geometric probability, and curvature-dependent probabilistic structure includes the following works:

* Augustin, T.; Coolen, F. P. A.; de Cooman, G.; Troffaes, M. C. M. ''Introduction to Imprecise Probabilities''. Wiley, 2014.

* Baryshnikov, Y.; Cao, Y.; Kahle, M.; Liu, J. (2024). ''Buffon’s problem on curved surfaces and Gaussian curvature''. ''Journal of Applied Probability''. Cambridge University Press. doi:10.1017/jpr.2024.19

* Herron, T.; Seidenfeld, T.; Wasserman, L. ''Divisive Conditioning: Further Results on Dilation''. Philosophy of Science, Vol. 64, No. 3, 1997.

* Herron, T.; Seidenfeld, T.; Wasserman, L. ''Distention for Sets of Probabilities''. Annals of Mathematics and Artificial Intelligence, Vol. 45, 2005.

* Moral, S.; Wilson, N. ''Dilation Properties of Coherent Nearly-Linear Models''. International Journal of Approximate Reasoning, Vol. 45, 2007.

* Shannon, C. E. (1948). ''A Mathematical Theory of Communication''. ''Bell System Technical Journal'', 27(3), 379–423; 27(4), 623–656.

== Copyright and licensing ==

Text and original figures © Howard Richardson.

Licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Reuse permitted with attribution.</text>
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        <id>2995240</id>
      </contributor>
      <minor />
      <comment>Request for proofreading.</comment>
      <origin>2815764</origin>
      <model>wikitext</model>
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      <text bytes="36306" sha1="307c1o530ypwhychpn1dttdn727rh5b" xml:space="preserve">{{Research project}}
{{Original research}}
{{To be peer reviewed}}

{{subst:proofread}}

== Research abstract ==
'''Probability Dilation Theory (PDT)''' is a measure-theoretic research framework for studying how probability measures transform under '''positive reweighting (dilation)''' while preserving normalization and producing controlled changes in expectation values.

The theory is an exploratory framework for iterative probability-measure evolution under positive dilation fields. The framework studies how repeated probabilistic reweighting transformations may generate emergent statistical structure, entropy flow, and multiscale probability dynamics.

At its core, PDT studies how repeated positive probability reweighting transformations alter the long-term structure of probability distributions.
PDT treats a probability measure as the primary mathematical object and investigates:
* invariant identities induced by reweighting,
* composition and iteration of dilations,
* fixed points and near-fixed behavior,
* whether iterative measure updates can generate testable multiscale statistical structure (to be evaluated via explicit models and simulations).

PDT is presented as a mathematical framework. Any proposed application to physics or cosmology must be expressed as a concrete model (space, baseline measure, dilation field) and tested against falsifiable predictions.

== Overview ==
PDT is motivated by the observation that some structural information can be recovered from sampling statistics (e.g., [[w:Buffon's needle problem|Buffon’s needle]]). PDT abstracts this idea by focusing on measure transformation itself: a dilation field modifies a baseline probability measure in a way that is:
* mathematically well-defined (positivity and normalization),
* composable under iteration,
* analyzable for invariants and fixed points.
=== Conceptual interpretation ===

A simplified conceptual flow of the PDT framework is:

&lt;pre&gt;
Baseline probability measure P
            ↓
Positive dilation field D(x)
            ↓
Reweighted probability measure P~
            ↓
Observable statistical changes
&lt;/pre&gt;
Repeated dilation may qualitatively behave as:

&lt;pre&gt;
Broad initial distribution
        ↓
Localized reweighting
        ↓
Probability concentration
        ↓
Emergent multiscale structure
&lt;/pre&gt;

Different classes of dilation fields may therefore generate qualitatively different long-term probability dynamics.
In this interpretation, PDT does not alter the underlying sample space directly. Instead, it modifies how probability mass is distributed across that space through a positive reweighting field.

Regions with larger values of the dilation field contribute more strongly to the transformed measure, while normalization preserves total probability. Earlier exploratory formulations of Probability Dilation Theory (PDT) were informally referred to as the Einstein Buffon Process (EBP), reflecting initial probabilistic-geometric interpretations inspired by Buffon-type constructions and Einstein-style scaling analogies. The framework has since evolved toward a broader iterative theory of probability-measure dynamics under positive dilation fields. A simple iterative interpretation may also be visualized as:

&lt;pre&gt;
P₀
 ↓ D₁
P₁
 ↓ D₂
P₂
 ↓ D₃
P₃
 ↓ ⋯
&lt;/pre&gt;

where each dilation field reweights the probability structure generated by the previous step.

Different classes of dilation fields may therefore generate qualitatively different long-term probability dynamics.

= Mathematical framework =

== Definitions and notation ==
Let &lt;math&gt;(\Omega,\Sigma)&lt;/math&gt; be a measurable space.

* &lt;math&gt;P&lt;/math&gt; denotes a probability measure on &lt;math&gt;(\Omega,\Sigma)&lt;/math&gt;.
* If &lt;math&gt;P&lt;/math&gt; has a density &lt;math&gt;p&lt;/math&gt; with respect to a reference measure &lt;math&gt;\mu&lt;/math&gt;, then &lt;math&gt;dP=p\,d\mu&lt;/math&gt;.
* &lt;math&gt;D:\Omega\to(0,\infty)&lt;/math&gt; is a measurable '''dilation field''' (a positive weight function).
* &lt;math&gt;Z(P,D)&lt;/math&gt; is the normalization constant:
.&lt;math&gt;
Z(P,D)=\int_\Omega D\,dP
&lt;/math&gt;
* For an observable &lt;math&gt;f:\Omega\to\mathbb{R}&lt;/math&gt; integrable under the relevant measure,
&lt;math&gt;
\mathbb{E}_P[f]
=
\int_\Omega f\,dP
&lt;/math&gt;.

== PDT transformation (probability reweighting) ==

Given &lt;math&gt;P&lt;/math&gt; and &lt;math&gt;D&lt;/math&gt; with &lt;math&gt;0&lt;Z(P,D)&lt;\infty&lt;/math&gt;, define the '''PDT transform''' &lt;math&gt;\widetilde{P}=\mathrm{PDT}(P;D)&lt;/math&gt; by:

&lt;math&gt;
\widetilde{P}(A)
=
\frac{
\int_A D\,dP
}{
\int_\Omega D\,dP
}
\quad\text{for all }A\in\Sigma
&lt;/math&gt;

If &lt;math&gt;dP=p\,d\mu&lt;/math&gt;, then &lt;math&gt;d\widetilde{P}=\widetilde{p}\,d\mu&lt;/math&gt;, where

&lt;math&gt;
\widetilde{p}(x)
=
\frac{D(x)\,p(x)}{Z}
&lt;/math&gt;

and

&lt;math&gt;
Z
=
\int_\Omega D(x)\,p(x)\,d\mu
&lt;/math&gt;

'''Interpretation:''' the dilation field &lt;math&gt;D&lt;/math&gt; shifts probability mass toward regions where &lt;math&gt;D&lt;/math&gt; is larger, while renormalization keeps total probability equal to 1.

PDT is mathematically related to importance sampling, Gibbs-style reweighting, and Radon–Nikodym measure transformations, although the framework emphasizes compositional and geometric interpretations of probability reweighting rather than only numerical estimation procedures.

Unlike conventional importance sampling, however, PDT emphasizes the compositional and potentially dynamical behavior of repeated probability reweighting transformations.
A familiar physical example of a strictly positive factor is the Lorentz factor:

&lt;math&gt;
\gamma(v)
=
\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}
&lt;/math&gt;

for

&lt;math&gt;
|v|&lt;c
&lt;/math&gt;

Lorentz contraction for a rod of rest length &lt;math&gt;L_0&lt;/math&gt; moving at speed &lt;math&gt;v&lt;/math&gt; is:

&lt;math&gt;
L(v)=\frac{L_0}{\gamma(v)}
&lt;/math&gt;

To connect this idea to PDT (as an illustration only), one may define a positive dilation field based on &lt;math&gt;\gamma&lt;/math&gt;.

== Worked finite example ==

Consider a finite probability space:

&lt;math&gt;
\Omega=\{a,b,c\}
&lt;/math&gt;

with baseline probabilities:

&lt;math&gt;
P(a)=0.2,\quad
P(b)=0.3,\quad
P(c)=0.5
&lt;/math&gt;

Define a positive dilation field:

&lt;math&gt;
D(a)=1,\quad
D(b)=2,\quad
D(c)=4
&lt;/math&gt;

The normalization constant is:

&lt;math&gt;
Z=\sum_x D(x)P(x)
&lt;/math&gt;

giving:

&lt;math&gt;
Z=(1)(0.2)+(2)(0.3)+(4)(0.5)=2.8
&lt;/math&gt;

The PDT-transformed probabilities become:

&lt;math&gt;
\widetilde{P}(a)=\frac{0.2}{2.8}\approx0.071
&lt;/math&gt;

&lt;math&gt;
\widetilde{P}(b)=\frac{0.6}{2.8}\approx0.214
&lt;/math&gt;

&lt;math&gt;
\widetilde{P}(c)=\frac{2.0}{2.8}\approx0.714
&lt;/math&gt;

This illustrates how PDT shifts probability mass toward regions with larger dilation weights while preserving normalization.

== Composition of dilations ==

An important structural property of sequential PDT transformations is that compose multiplicatively.

Suppose two positive dilation fields:

&lt;math&gt;
D_1(x)&gt;0
&lt;/math&gt;

and

&lt;math&gt;
D_2(x)&gt;0
&lt;/math&gt;

are applied successively to a baseline probability measure &lt;math&gt;P&lt;/math&gt;.

The first dilation produces:

&lt;math&gt;
\widetilde{P}_1(A)
=
\frac{\int_A D_1\,dP}
{\int_\Omega D_1\,dP}
&lt;/math&gt;

Applying the second dilation field to &lt;math&gt;\widetilde{P}_1&lt;/math&gt; gives:

&lt;math&gt;
\widetilde{P}_2(A)
=
\frac{\int_A D_2\,d\widetilde{P}_1}
{\int_\Omega D_2\,d\widetilde{P}_1}
&lt;/math&gt;

Substituting the first transformation into the second yields:

&lt;math&gt;
\widetilde{P}_2(A)
=
\frac{
\int_A D_2D_1\,dP
}{
\int_\Omega D_2D_1\,dP
}
&lt;/math&gt;

This shows that sequential PDT transformations compose through multiplication of the dilation fields.

This compositional structure allows iterative probability reweighting to be studied using products of positive fields, potentially generating multiscale or hierarchical probability structures under repeated application.

== Fixed points and iterative dynamics ==

An important question in PDT concerns the long-term behavior of repeated PDT transformations.

Given an initial probability measure:

&lt;math&gt;
P_0
&lt;/math&gt;

and a sequence of positive dilation fields:

&lt;math&gt;
D_1,D_2,D_3,\dots
&lt;/math&gt;

successive PDT transformations generate a sequence of measures:

&lt;math&gt;
P_0
\rightarrow
P_1
\rightarrow
P_2
\rightarrow
P_3
\rightarrow \cdots
&lt;/math&gt;

where each transformed measure is obtained by reweighting the previous one.

A measure &lt;math&gt;P&lt;/math&gt; is called a fixed point of a dilation field &lt;math&gt;D&lt;/math&gt; if:

&lt;math&gt;
\widetilde{P}=P
&lt;/math&gt;

under the PDT transformation.

In the simplest case, this requires the dilation field to be constant almost everywhere with respect to &lt;math&gt;P&lt;/math&gt;. More general fixed-point behavior may arise when iterative compositions balance probability amplification against normalization.

More generally, repeated compositions of nontrivial dilation fields may generate:

* hierarchical probability structure;
* multiscale statistical behavior;
* attractor-like distributions;
* approximately stable transformed measures.

These questions connect PDT to broader areas of:

* dynamical systems;
* stochastic processes;
* iterative renormalization methods;
* probabilistic geometry.

At present these iterative properties remain largely unexplored within the PDT framework.

== Entropy and iterative probability flow ==

Repeated PDT transformations may alter the entropy structure of a probability measure.

For a discrete probability distribution:

&lt;math&gt;
P=\{p_i\}
&lt;/math&gt;

the Shannon entropy is:

&lt;math&gt;
H(P)
=
-\sum_i p_i \log p_i
&lt;/math&gt;

Under iterative PDT transformation, successive transformed measures:

&lt;math&gt;
P_0
\rightarrow
P_1
\rightarrow
P_2
\rightarrow \cdots
&lt;/math&gt;

may exhibit changing entropy behavior depending on the structure of the dilation fields.

For example:
* strongly localized dilation fields may concentrate probability mass and reduce entropy;
* broader or smoothing dilation fields may distribute probability more evenly and increase entropy;
* iterative compositions may generate approximately stable entropy profiles.

These questions connect PDT to:
* information theory,
* statistical mechanics,
* stochastic dynamics,
* and renormalization-style iterative systems.

At present the entropy behavior of iterative PDT transformations remains an open area for investigation.

== Toy experiment: entropy under repeated dilation ==

A simple finite-state experiment illustrates how repeated PDT transformations can change the entropy of a probability distribution.

Let the initial probability distribution be:

&lt;math&gt;
P_0=(0.2,0.2,0.2,0.2,0.2)
&lt;/math&gt;

and define a positive dilation field:

&lt;math&gt;
D=(1,1,2,4,8)
&lt;/math&gt;

At each step, apply the PDT update:

&lt;math&gt;
P_{n+1}(i)
=
\frac{D(i)P_n(i)}
{\sum_j D(j)P_n(j)}
&lt;/math&gt;

The Shannon entropy is:

&lt;math&gt;
H(P_n)
=
-\sum_i P_n(i)\log P_n(i)
&lt;/math&gt;

In this toy model, repeated dilation shifts probability mass toward the highest-weight state. Over ten iterations, the entropy decreases from approximately:

&lt;math&gt;
H(P_0)\approx1.6094
&lt;/math&gt;

to:

&lt;math&gt;
H(P_{10})\approx0.00775
&lt;/math&gt;

The final distribution is approximately:

&lt;math&gt;
P_{10}
\approx
(0.000000001,\;0.000000001,\;0.000000953,\;0.000975609,\;0.999023437)
&lt;/math&gt;

This example demonstrates probability concentration under repeated positive dilation. It is a finite-state toy model and should not be interpreted as physical evidence; its purpose is to illustrate iterative PDT behavior.
== Mathematical context ==
PDT transformations may be viewed as exploratory probability-measure reweighting procedures related conceptually to conditioning behavior, stochastic transformations, entropy evolution, and probabilistic dilation phenomena studied in imprecise probability theory and dynamical systems literature.
In PDT, the term ''dilation'' refers to probabilistic reweighting and transformation behavior under localized weighting fields rather than the formal operator-theoretic notion of dilation used in functional analysis.
The iterative entropy-flow experiments explored in PDT resemble finite-state dynamical systems in which repeated transformations generate convergence, concentration, and emergent probabilistic structure over successive iterations.
=== Example entropy evolution ===

{| class=&quot;wikitable&quot;
! Iteration !! Shannon entropy
|-
| 0 || 1.6094
|-
| 1 || 1.2990
|-
| 2 || 0.7790
|-
| 3 || 0.4399
|-
| 5 || 0.1500
|-
| 10 || 0.0078
|}
Entropy evolution under repeated localized PDT transformation showing entropy reduction and probability concentration under iterative probabilistic reweighting. Programmatically generated using Python in a ChatGPT-assisted workflow. The entropy decreases under repeated application of the dilation field as probability mass becomes increasingly concentrated in the highest-weight states.
=== Localized dilation fields ===

A useful class of PDT transformations is generated by localized positive dilation fields.

Consider a one-dimensional finite configuration space with states indexed by:

&lt;math&gt;
x=0,1,2,\dots,N
&lt;/math&gt;

and define a localized dilation field centered at &lt;math&gt;x_0&lt;/math&gt;:

&lt;math&gt;
D(x)
=
\exp\!\left(
\lambda
\exp\!\left(
-\frac{(x-x_0)^2}{2\sigma^2}
\right)
\right)
&lt;/math&gt;

where:

* &lt;math&gt;\lambda&gt;0&lt;/math&gt; controls the strength of the dilation;
* &lt;math&gt;\sigma&lt;/math&gt; controls the spatial width of the localized field.

Narrow values of &lt;math&gt;\sigma&lt;/math&gt; produce sharply localized amplification, while broader values produce smoother probability reweighting across the configuration space.

Under iterative PDT dynamics:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D(x)P_n(x)
}{
\sum_y D(y)P_n(y)
}
&lt;/math&gt;

the probability distribution may progressively concentrate near the center of the dilation field.

=== Example entropy evolution for localized fields ===

Using an initially uniform distribution over 21 states and iterating the PDT transformation 10 times produces the following representative entropy behavior:

{| class=&quot;wikitable&quot;
! Field width &lt;math&gt;\sigma&lt;/math&gt;
! Final entropy after 10 iterations
! Maximum probability after 10 iterations
|-
| 1.5 || 0.0352 || 0.9950
|-
| 3.0 || 0.8162 || 0.7141
|-
| 6.0 || 1.5367 || 0.3595
|}
[[File:PDT entropy evolution localized field.png|thumb|center|600px|Entropy evolution under repeated localized PDT transformation showing entropy reduction and probability concentration under iterative probabilistic reweighting.]]
[[File:Epd_entropy_evolution.png|thumb|center|600px|Entropy evolution under repeated localized PDT dilation. Narrow localized dilation fields produce rapid entropy reduction and probability concentration under iterative reweighting.]]
These results indicate that narrower localized dilation fields generate stronger probability concentration and more rapid entropy reduction.

== Comparative entropy-flow experiments ==

The following finite-state computational experiments illustrate comparative entropy evolution under several classes of PDT dilation fields. Each experiment begins with the same initially uniform probability distribution and applies repeated PDT transformations under different field structures. The experiments are exploratory and intended to illustrate qualitative differences in iterative probabilistic behavior rather than empirical physical predictions.
{| class=&quot;wikitable&quot;
|+ Comparative entropy-flow behavior under PDT field classes
! Field class
! Final entropy
! Entropy decrease
! Final max probability
! Qualitative behavior
|-
| Localized
| 0.3104
| 3.4032
| 0.9275
| Strong probability concentration
|-
| Oscillatory
| 1.5779
| 2.1357
| 0.3418
| Distributed oscillatory structure
|-
| Multi-peak
| 0.2851
| 3.4284
| 0.9425
| Multiple concentration regions
|-
| Stochastic
| 0.7744
| 2.9392
| 0.7413
| Fluctuating concentration behavior
|}
These experiments suggest that different classes of dilation fields may generate qualitatively distinct entropy-flow and concentration behavior under iterative PDT dynamics. Localized and multi-peak fields produce strong entropy reduction and probability concentration, while oscillatory fields preserve more distributed probabilistic structure. Stochastic fields exhibit fluctuating but still partially concentrating behavior in this finite-state example.
In this toy model, repeated localized dilation behaves qualitatively like an attractor centered on the highest-weight region of the configuration space.
[[File:Pdt comparative entropy flow.png|thumb|Comparative entropy evolution under localized, oscillatory, multi-peak, and stochastic PDT dilation fields.]]
The experiment is intended only as a finite-state demonstration of iterative PDT dynamics and should not be interpreted as physical evidence.

=== Oscillatory dilation fields ===

Another useful class of PDT transformations is generated by oscillatory positive dilation fields.

One example is:

&lt;math&gt;
D(x)
=
\exp(\lambda\sin(kx))
&lt;/math&gt;

where:

* &lt;math&gt;\lambda&gt;0&lt;/math&gt; controls the strength of the oscillatory amplification;
* &lt;math&gt;k&lt;/math&gt; controls the spatial frequency of the oscillation.

Because the exponential is always positive, the dilation field remains strictly positive for all states.

Unlike localized dilation fields, oscillatory fields may generate multiple competing high-weight regions across the configuration space.

Under repeated PDT transformation:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D(x)P_n(x)
}{
\sum_y D(y)P_n(y)
}
&lt;/math&gt;

probability mass may evolve toward several distributed concentration regions rather than a single dominant attractor.

=== Example oscillatory-field experiment ===

A finite-state experiment was performed using:

* 41 discrete states;
* an initially uniform probability distribution;
* a positive oscillatory dilation field with three spatial oscillation cycles;
* 10 successive PDT iterations.

Representative entropy behavior was:

{| class=&quot;wikitable&quot;
! Iteration
! Shannon entropy
|-
| 0 || 3.7136
|-
| 2 || 2.8699
|-
| 5 || 2.3018
|-
| 10 || 1.9335
|}

Unlike sharply localized dilation fields, the oscillatory field produced slower entropy reduction and multiple probability concentration peaks distributed across the configuration space.

After 10 iterations, the largest probability concentration remained distributed rather than collapsing into a single dominant state.

This suggests that different classes of positive dilation fields may generate qualitatively different long-term iterative probability structures.

The experiment is intended only as a finite-state demonstration of iterative PDT dynamics and should not be interpreted as physical evidence.
=== Multi-peak localized dilation fields ===

A broader class of PDT transformations may be generated using multiple localized dilation peaks distributed across the configuration space.

One example is:

&lt;math&gt;
D(x)
=
\exp\!\left(
\sum_k
\lambda_k
\exp\!\left(
-\frac{(x-x_k)^2}{2\sigma_k^2}
\right)
\right)
&lt;/math&gt;

where:

* &lt;math&gt;x_k&lt;/math&gt; are the locations of the dilation peaks;
* &lt;math&gt;\lambda_k&gt;0&lt;/math&gt; control the amplification strength of each peak;
* &lt;math&gt;\sigma_k&lt;/math&gt; control the spatial width of each localized region.

This construction generates a positive multimodal dilation landscape containing several competing amplification regions.

Under repeated PDT iteration:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D(x)P_n(x)
}{
\sum_y D(y)P_n(y)
}
&lt;/math&gt;

probability mass may evolve toward multiple partially localized concentration regions.

Unlike single localized dilation fields, multi-peak fields may generate:

* competing attractor-like regions;
* hierarchical probability concentration;
* partially stabilized multimodal distributions;
* multiscale probability structure.

Depending on the relative strengths and widths of the peaks, the iterative dynamics may favor:
* dominance by a single peak;
* coexistence of several concentration regions;
* or slowly evolving metastable probability structures.

=== Conceptual interpretation ===

A qualitative iterative evolution may be visualized as:

&lt;pre&gt;
Broad initial distribution
        ↓
Multiple localized amplifications
        ↓
Competing concentration regions
        ↓
Emergent multimodal probability structure
&lt;/pre&gt;

This class of dilation fields suggests that iterative PDT dynamics may generate richer probability organization than either single localized attractors or simple oscillatory fields alone.

At present these behaviors remain exploratory computational observations within finite-state toy models.
=== Random and stochastic dilation fields ===

Another important class of PDT transformations arises when the dilation field itself varies stochastically.

A simple stochastic dilation field may be written schematically as:

&lt;math&gt;
D_n(x)
=
\exp\!\left(
\sigma \eta_n(x)
\right)
&lt;/math&gt;

where:

* &lt;math&gt;\eta_n(x)&lt;/math&gt; is a random field or stochastic fluctuation at iteration &lt;math&gt;n&lt;/math&gt;;
* &lt;math&gt;\sigma&gt;0&lt;/math&gt; controls the strength of the stochastic variation.

Because the exponential is strictly positive, the dilation field remains positive for all realizations of the random process.

Under repeated PDT iteration:

&lt;math&gt;
P_{n+1}(x)
=
\frac{
D_n(x)P_n(x)
}{
\sum_y D_n(y)P_n(y)
}
&lt;/math&gt;

the probability landscape itself fluctuates dynamically from one iteration to the next.

Unlike deterministic localized or oscillatory dilation fields, stochastic dilation fields may generate:

* fluctuating concentration regions;
* transient attractor-like structures;
* noise-driven entropy evolution;
* intermittent probability concentration;
* metastable probabilistic configurations.

=== Conceptual interpretation ===

A qualitative stochastic evolution may be visualized as:

&lt;pre&gt;
Broad initial distribution
        ↓
Random localized amplification
        ↓
Fluctuating concentration regions
        ↓
Dynamic probabilistic structure
&lt;/pre&gt;

Depending on the stochastic process used to generate the dilation fields, the long-term dynamics may exhibit:
* partial concentration,
* persistent fluctuations,
* stochastic stabilization,
* or continuously evolving probabilistic structure.

These ideas connect PDT to broader areas of:
* stochastic processes;
* random multiplicative systems;
* statistical mechanics;
* noise-driven dynamical systems;
* probabilistic geometry.

At present these behaviors remain exploratory computational possibilities within finite-state toy models.

== Qualitative classes of iterative PDT behavior ==

Different classes of positive dilation fields may generate qualitatively different long-term probability dynamics under repeated PDT transformation.

The following table summarizes several representative classes explored within finite-state toy models.

{| class=&quot;wikitable&quot;
! Dilation-field class
! Typical iterative behavior
! Representative qualitative structure
|-
| Localized fields
| Strong entropy reduction and concentration toward a dominant region
| Single attractor-like concentration
|-
| Oscillatory fields
| Distributed amplification with slower entropy reduction
| Patterned multimodal structure
|-
| Multi-peak localized fields
| Competition between several concentration regions
| Hierarchical or metastable probability structure
|-
| Random and stochastic fields
| Fluctuating amplification and noise-driven evolution
| Dynamic probabilistic landscapes
|}

These examples suggest that iterative PDT reweighting may generate a broad spectrum of emergent statistical structures depending on the geometry and dynamics of the dilation field.

Within the PDT framework, the iterative behavior of probability measures may therefore depend as strongly on the structure of the dilation field as on the initial probability distribution itself.

At present these qualitative behaviors remain exploratory computational observations within finite-state toy models.

== Numerical simulation and iterative models ==

=== Simulation model description ===

In discrete demonstrations, the “state space” may be represented by a finite set such as bins, configurations, or catalog points.

Two equivalent discrete implementations are common:

* '''weighted evaluation''': retain all points and assign weights proportional to &lt;math&gt;D&lt;/math&gt;;
* '''importance resampling''': generate a new empirical catalog with sampling probabilities proportional to &lt;math&gt;D&lt;/math&gt;.

=== Demonstration: reweighting mock galaxy catalogs ===

A simple computational demonstration of PDT may be constructed using synthetic galaxy catalogs in a periodic simulation box.

The demonstration pipeline is:

# generate a baseline mock catalog;
# define a positive dilation field over the configuration space;
# perform PDT-style importance resampling;
# compute the resulting two-point correlation function &lt;math&gt;\xi(r)&lt;/math&gt;;
# compare transformed and baseline catalogs.

One example dilation field is:

&lt;math&gt;
D(x)=\exp(\lambda\phi(x))
&lt;/math&gt;

where:

* &lt;math&gt;\lambda&gt;0&lt;/math&gt; controls the strength of the dilation;
* &lt;math&gt;\phi(x)\ge0&lt;/math&gt; is a nonnegative configuration-space field.

An example seed-field construction is:

&lt;math&gt;
\phi(x)=\sum_k \exp\!\left(-\frac{\|x-s_k\|^2}{2\sigma^2}\right)
&lt;/math&gt;

where &lt;math&gt;s_k&lt;/math&gt; are seed locations and &lt;math&gt;\sigma&lt;/math&gt; controls the width of the seed influence.

The two-point correlation function may be estimated using the normalized Landy–Szalay estimator:

&lt;math&gt;
\xi(r)
=
\frac{DD(r)-2DR(r)+RR(r)}{RR(r)}
&lt;/math&gt;

where &lt;math&gt;DD&lt;/math&gt;, &lt;math&gt;DR&lt;/math&gt;, and &lt;math&gt;RR&lt;/math&gt; are normalized pair counts.

{{Note|Unless observational datasets are explicitly supplied, demonstrations may use synthetic target correlation curves for methodological illustration only. Synthetic demonstrations should not be interpreted as empirical cosmological evidence.}}

When run using synthetic target curves, PDT-resampled catalogs may exhibit enhanced small-scale clustering relative to the baseline configuration.

=== Computational demonstrations ===

Reference implementations and supplementary simulation notebooks may be maintained on external repositories or supplementary Wikiversity pages.

{{collapse top|Python demonstration placeholder}}

&lt;syntaxhighlight lang=&quot;python&quot;&gt;
# Example implementations may be maintained separately
# on GitHub, OSF, or supplementary Wikiversity pages.
&lt;/syntaxhighlight&gt;

{{collapse bottom}}


== Scope and Limitations ==

PDT is a mathematical framework for measure transformations. It does not claim:

* a replacement theory for General Relativity or Quantum Mechanics;
* empirical confirmation without explicit predictions and tests;
* observational validation without independently reproducible analysis.

The following discussion extends beyond the primary mathematical framework developed earlier in the article and explores possible conceptual implications and speculative generalizations.

== Speculative Extensions and Geometric Renormalization ==

''This section is speculative and exploratory in nature.''

Recent mathematical work published in the ''Journal of Applied Probability'' by Baryshnikov, Cao, Kahle, and Liu suggests a possible connection between probability distributions and intrinsic geometry.

Studies of “Buffon deficits” on curved manifolds indicate that deviations from classical flat-space Buffon probabilities may encode curvature-dependent geometric information. Within the PDT framework, these observations motivate the broader possibility that geometric structure may influence iterative probabilistic dynamics through curvature-dependent statistical weighting effects.
Within PDT, these results are conceptually relevant because they suggest that probabilistic weighting structures may encode nontrivial geometric information. In particular, the Cambridge analysis demonstrates that generalized Buffon-type probabilistic constructions can reflect Gaussian curvature in different geometries. PDT extends this probabilistic perspective by exploring how iterative probability-measure transformations under positive dilation fields may generate evolving statistical structure, entropy flow, and geometry-dependent probabilistic behavior under repeated transformation.
At present these ideas remain exploratory and heuristic. No direct physical interpretation is presently established within the PDT framework. Within the PDT framework, this motivates the speculative possibility that curvature could act as a statistical weighting mechanism on classes of admissible paths or configurations.

== Future directions ==

* develop canonical families of dilation fields and invariants;
* clarify “structure-from-measure” diagnostics;
* publish reproducible simulation notebooks and parameter sweeps;
* compare multiple dilation families under shared evaluation criteria;
* investigate connections between probabilistic geometry and curvature-dependent statistical measures.
== Future Directions: Probability Element (PE) ==

A speculative extension of Probability Dilation Theory (PDT) is the introduction of a minimal invariant scale in probability-state space, referred to as a '''Probability Element (PE)'''. This concept lies outside standard Fisher information geometry and is not part of established physics.

The PE hypothesis proposes that probability-state space may not be fully continuous, but may instead admit a smallest distinguishable scale of structure in terms of information-theoretic resolution.

This can be expressed in terms of a dimensionless ratio:

&lt;math&gt;\eta = \frac{\sigma_P}{\sigma}&lt;/math&gt;

where:

&lt;math&gt;\sigma_P&lt;/math&gt; is a hypothesized minimal probability-resolution scale,
&lt;math&gt;\sigma&lt;/math&gt; is an effective distinguishability scale in probability-state space.

=== Conceptual motivation ===

Standard Fisher information geometry treats probability distributions as points on a smooth manifold with arbitrarily fine distinguishability. The PE hypothesis explores the possibility that this distinguishability may have a lower bound, introducing a form of discreteness in probability-state geometry.

=== Illustrative toy model (not derived physics) ===

As a heuristic example, one may consider a modification to special relativistic time dilation of the form:

&lt;math&gt;d\tau = dt\sqrt{1 - \frac{v^2}{c^2}}\sqrt{1 - \eta^2}&lt;/math&gt;

where:

&lt;math&gt;v&lt;/math&gt; is velocity,
&lt;math&gt;c&lt;/math&gt; is the speed of light,
&lt;math&gt;\eta = \sigma_P / \sigma&lt;/math&gt; encodes a proposed probability-resolution scale.

This expression is constructed such that standard special relativity is recovered exactly in the limit &lt;math&gt;\eta \to 0&lt;/math&gt;.

=== Status ===

The Probability Element concept is:

Not part of standard Fisher information geometry
not derived from quantum mechanics or general relativity
not currently empirically established.

It is included only as a speculative direction for exploring whether probability-state space admits a minimal geometric resolution scale.

=== Open questions ===

Key open research directions include:

Whether a consistent discrete formulation of probability geometry can be constructed.

Whether a fundamental probability-resolution scale &lt;math&gt;\sigma_P&lt;/math&gt; can be derived from known physical principles.

Whether such a structure could lead to measurable deviations from standard statistical or relativistic predictions.

== Convergence behavior ==

Iterative PDT transformations may exhibit qualitatively different convergence behavior depending on the structure of the applied dilation field. Repeated probabilistic reweighting can produce entropy reduction, probability concentration, oscillatory behavior, or fluctuating stochastic dynamics over successive iterations.

=== Qualitative convergence classes ===

Exploratory finite-state PDT experiments suggest several broad classes of iterative behavior:

* '''Concentrating regimes''' — repeated transformations progressively concentrate probability mass into localized regions, often accompanied by decreasing Shannon entropy.

* '''Oscillatory regimes''' — probability structure evolves through recurring redistribution patterns without strong long-term concentration.

* '''Multi-peak regimes''' — multiple semi-stable concentration regions emerge simultaneously, producing persistent structured probability distributions.

* '''Stochastic regimes''' — fluctuating probabilistic structure evolves under partially random or time-dependent weighting behavior.

=== Entropy and convergence ===

In many exploratory PDT experiments, entropy reduction correlates with increasing probability concentration under repeated transformation. However, some oscillatory and stochastic field classes may preserve higher entropy distributions or exhibit fluctuating convergence behavior over time.

The relationship between entropy evolution and convergence remains an open area of investigation. Future work may examine entropy rates, stability properties, and long-term probabilistic structure under repeated PDT transformations.

=== Attractor-like behavior ===

Some iterative PDT systems may exhibit transient attractor-like probabilistic structure in finite-state computational experiments. These behaviors are presently exploratory and are not established mathematical attractors in the formal dynamical-systems sense.

Future investigation of PDT convergence behavior may include stability analysis, fixed-point structure, stochastic convergence properties, and comparison with established dynamical systems and probabilistic evolution frameworks.

== Current limitations ==
PDT presently operates as an exploratory probabilistic and computational framework. The theory does not presently derive known physical laws from first principles, nor does it replace established formulations of quantum mechanics or general relativity. Current PDT investigations primarily focus on iterative probability transformations, entropy evolution, probabilistic weighting behavior, and computationally modeled structure formation.
Many proposed physical interpretations associated with PDT remain speculative and exploratory. Existing computational experiments are finite-state toy models intended to illustrate qualitative probabilistic behavior rather than experimentally verified physical mechanisms.
Future development of PDT would likely require additional mathematical formalization, convergence analysis, stochastic modeling, and comparison with established probabilistic and dynamical systems frameworks.

== See also ==

* [[w:Buffon's needle problem|Buffon's needle problem]]
* [[w:Probability measure|Probability measure]]
* [[w:Importance sampling|Importance sampling]]
* [[w:Radon–Nikodym theorem|Radon–Nikodym theorem]]
* [[w:Dynamical system|Dynamical systems]]

* [[w:Entropy (information theory)|Entropy]]
* [[w:Information theory|Information theory]]
* [[w:Measure theory|Measure theory]]
* [[w:Geometric probability|Geometric probability]]

* [[w:Shannon entropy|Shannon entropy]]
* [[w:Stochastic process|Stochastic process]]
* [[w:Fixed point (mathematics)|Fixed point]]
* [[w:Convergence (mathematics)|Convergence]]

== Future research directions ==

Exploratory subpages associated with Probability Dilation Theory (PDT) include:

* [[/Quantum Computing in Dilation Fields|Quantum computing in dilation fields]]
* [[/Fisher Geometry and Dilation Flows|Fisher geometry and dilation flows]]

== Related probabilistic and geometric literature ==

Related literature on probabilistic dilation, conditioning behavior, geometric probability, and curvature-dependent probabilistic structure includes the following works:

* Augustin, T.; Coolen, F. P. A.; de Cooman, G.; Troffaes, M. C. M. ''Introduction to Imprecise Probabilities''. Wiley, 2014.

* Baryshnikov, Y.; Cao, Y.; Kahle, M.; Liu, J. (2024). ''Buffon’s problem on curved surfaces and Gaussian curvature''. ''Journal of Applied Probability''. Cambridge University Press. doi:10.1017/jpr.2024.19

* Herron, T.; Seidenfeld, T.; Wasserman, L. ''Divisive Conditioning: Further Results on Dilation''. Philosophy of Science, Vol. 64, No. 3, 1997.

* Herron, T.; Seidenfeld, T.; Wasserman, L. ''Distention for Sets of Probabilities''. Annals of Mathematics and Artificial Intelligence, Vol. 45, 2005.

* Moral, S.; Wilson, N. ''Dilation Properties of Coherent Nearly-Linear Models''. International Journal of Approximate Reasoning, Vol. 45, 2007.

* Shannon, C. E. (1948). ''A Mathematical Theory of Communication''. ''Bell System Technical Journal'', 27(3), 379–423; 27(4), 623–656.

== Copyright and licensing ==

Text and original figures © Howard Richardson.

Licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Reuse permitted with attribution.</text>
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      <text bytes="75127" sha1="gkm83219k6cenh3bmp6x3uptix0v218" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 30° turns.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_1&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_1&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 12° turns.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in completely orthogonal invariant square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation in completely orthogonal great square invariant planes, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The &lt;math&gt;r_7&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_1&lt;/math&gt; chord.  The rotational curve over each 90° &lt;math&gt;r_1&lt;/math&gt; chord makes just one 45° turn. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;\tfrac{15\pi}{2}&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically in invariant hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once.    

In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.   

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="75266" sha1="sb96f306gpaw4hr4kz67rlr8o6wjqrl" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 30° turns.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_1&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_1&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 12° turns.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking great square planes to each other, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once.    

In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.   

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="75092" sha1="g4b5mc4mfc9crvlae19efxdtdiltj4y" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_1&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_1&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking great square planes to each other, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once.    

In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.   

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="75802" sha1="m8d4hr030ugrq2j51t6k6yfzt76bokh" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking great square planes to each other, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once.    

In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.   

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

In the 600-cell there is another distinct isoclinic rotation taking great decagon planes to each other, over &lt;math&gt;r_{12}=\tfrac{4\pi}{5}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="75918" sha1="9hl7fy8rcmg7h1shktna9c5up21nn0g" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking great square planes to each other, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\tfrac{4\pi}{5}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking great decagon planes to each other, over &lt;math&gt;r_{12}=\tfrac{4\pi}{5}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="75906" sha1="fppjubcrqspsod8lqnvzp1lszbjwf4i" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking great square planes to each other, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking great decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="77635" sha1="evvvh4irre6dw7u8ulw5ar9sv1byp2h" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
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|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
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|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
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|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation. 

[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 36° isoclinic rotation, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Each 36° isoclinic rotational displacement takes every great decagon plane to a great decagon plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>evvvh4irre6dw7u8ulw5ar9sv1byp2h</sha1>
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      <text bytes="77638" sha1="3ztoxijln2qam8na3oqbvw6gg14hk0c" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation. 

[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

...In the 600-cell there is another distinct 36° isoclinic rotation, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Each 36° isoclinic rotational displacement takes every great decagon plane to a great decagon plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="77688" sha1="owlq9pzcf0towaxjgzpghsp97cumgta" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
...In the 600-cell there is another distinct 36° isoclinic rotation, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Each 36° isoclinic rotational displacement takes every great decagon plane to a great decagon plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="77826" sha1="1sud4y56bi6qu8rj6wx2ildttrk82ws" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
...In the 600-cell there is another distinct 36° isoclinic rotation, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Each 36° isoclinic rotational displacement takes every great decagon plane to a great decagon plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>1sud4y56bi6qu8rj6wx2ildttrk82ws</sha1>
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    <revision>
      <id>2815684</id>
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      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <text bytes="77816" sha1="8k8duxf8kk3bgcilylmm1heatnmxhr3" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 
In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.
The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation. 

...In the 600-cell there is another distinct 36° isoclinic rotation, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Each 36° isoclinic rotational displacement takes every great decagon plane to a great decagon plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>8k8duxf8kk3bgcilylmm1heatnmxhr3</sha1>
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      <id>2815707</id>
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      <timestamp>2026-06-14T23:23:37Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* The 600-cell */</comment>
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      <text bytes="76262" sha1="ejemtmp5lebz1ezc4c3xygqpnxsijhf" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
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| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
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|{{radic|2}}
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|- style=&quot;background: seashell;&quot; |
|1.414~
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|1.414~
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|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 

In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The invariant completely orthogonal central planes of this rotation each intersect only two vertices of the 600-cell. Each vertex makes two orbits of a great pentagon within the moving invariant plane in the course of one complete isoclinic revolution of period 5. The rotation takes disjoint 24-cells to each other. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. 24 Clifford parallel {5/2} pentagram geodesic isoclines of circumference &lt;math&gt;4\pi&lt;/math&gt; over five &lt;math&gt;r_{12}&lt;/math&gt; chords form a circular helix of 24 twisted parallel strands 4{30/12}=24{5/2} that visits each 600-cell vertex once.  


{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <id>2815740</id>
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      <contributor>
        <username>Dc.samizdat</username>
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      <text bytes="76278" sha1="ak1vqpsckcqmqc8fep3reumfjwnx84t" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell an isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 

In the 600-cell an isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The 12 invariant central planes of this rotation each intersect only two vertices of the 600-cell. Each vertex makes two orbits of a great pentagon within the moving invariant plane in the course of one complete isoclinic revolution of period 5. The 24 vertices are a 24-cell, and the rotation takes disjoint 24-cells to each other. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. 24 Clifford parallel {5/2} pentagram geodesic isoclines of circumference &lt;math&gt;4\pi&lt;/math&gt; over five &lt;math&gt;r_{12}&lt;/math&gt; chords form a circular helix of 24 twisted parallel strands 4{30/12}=24{5/2} that visits each 600-cell vertex once.  


{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>ak1vqpsckcqmqc8fep3reumfjwnx84t</sha1>
    </revision>
    <revision>
      <id>2815744</id>
      <parentid>2815740</parentid>
      <timestamp>2026-06-15T02:24:18Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* The 600-cell */</comment>
      <origin>2815744</origin>
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      <text bytes="76310" sha1="7cfrfd96lufeio2gjjkmp3a4byevhfg" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
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| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
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|{{radic|2}}
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|- style=&quot;background: seashell;&quot; |
|1.414~
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|1.414~
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|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell the characteristic isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 

In the 600-cell the characteristic isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The 12 invariant central planes of this rotation each intersect only two vertices of the 600-cell. Each vertex makes two orbits of a great pentagon within the moving invariant plane in the course of one complete isoclinic revolution of period 5. The 24 vertices are a 24-cell, and the rotation takes disjoint 24-cells to each other. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. 24 Clifford parallel {5/2} pentagram geodesic isoclines of circumference &lt;math&gt;4\pi&lt;/math&gt; over five &lt;math&gt;r_{12}&lt;/math&gt; chords form a circular helix of 24 twisted parallel strands 4{30/12}=24{5/2} that visits each 600-cell vertex once.  


{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>7cfrfd96lufeio2gjjkmp3a4byevhfg</sha1>
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      <text bytes="76272" sha1="iu1j1t341wdfg990uihf2dwjf454t5u" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell the characteristic isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. The skew {30}-gons have these chords:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 

In the 600-cell the characteristic isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The invariant central planes of this rotation each intersect only two vertices of the 600-cell. Each vertex makes two orbits of a great pentagon within the moving invariant plane in the course of one complete isoclinic revolution of period 5. The rotation takes disjoint 24-cells to each other. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. 24 Clifford parallel {5/2} pentagram geodesic isoclines of circumference &lt;math&gt;4\pi&lt;/math&gt; over five &lt;math&gt;r_{12}&lt;/math&gt; chords form a circular helix of 24 twisted parallel strands 4{30/12}=24{5/2} that visits each 600-cell vertex once.  


{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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    <revision>
      <id>2815757</id>
      <parentid>2815755</parentid>
      <timestamp>2026-06-15T02:45:56Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* The 600-cell */</comment>
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      <text bytes="76279" sha1="czawlhmlhgif07vqngbe0moxanlqpso" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
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| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
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|{{radic|2}}
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|- style=&quot;background: seashell;&quot; |
|1.414~
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|1.414~
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|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell the characteristic isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. In the skew {30}-gons the chord lengths are:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 

In the 600-cell the characteristic isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The invariant central planes of this rotation each intersect only two vertices of the 600-cell. Each vertex makes two orbits of a great pentagon within the moving invariant plane in the course of one complete isoclinic revolution of period 5. The rotation takes disjoint 24-cells to each other. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. 24 Clifford parallel {5/2} pentagram geodesic isoclines of circumference &lt;math&gt;4\pi&lt;/math&gt; over five &lt;math&gt;r_{12}&lt;/math&gt; chords form a circular helix of 24 twisted parallel strands 4{30/12}=24{5/2} that visits each 600-cell vertex once.  


{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>czawlhmlhgif07vqngbe0moxanlqpso</sha1>
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    <revision>
      <id>2815760</id>
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      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <text bytes="76292" sha1="7ge40n7wk0q7v2ke4j9aj9m3b3koeqm" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell the characteristic isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. In the skew {30}-gons the chord lengths are:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 

In the 600-cell the characteristic isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The 60 invariant central planes of this rotation each intersect only two antipodal vertices of the 600-cell. Each vertex makes two orbits of a great pentagon within the moving invariant plane in the course of one complete isoclinic revolution of period 5. The rotation takes disjoint 24-cells to each other. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. 24 Clifford parallel {5/2} pentagram geodesic isoclines of circumference &lt;math&gt;4\pi&lt;/math&gt; over five &lt;math&gt;r_{12}&lt;/math&gt; chords form a circular helix of 24 twisted parallel strands 4{30/12}=24{5/2} that visits each 600-cell vertex once.  


{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>7ge40n7wk0q7v2ke4j9aj9m3b3koeqm</sha1>
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    <revision>
      <id>2815771</id>
      <parentid>2815760</parentid>
      <timestamp>2026-06-15T03:19:52Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* The 600-cell */</comment>
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      <text bytes="76267" sha1="4680i9pcg6wth7d9q3um32tzqzprw03" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
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| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
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|{{radic|2}}
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|- style=&quot;background: seashell;&quot; |
|1.414~
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|1.414~
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|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which visits each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that visits each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that visits each 24-cell vertex once. 

In the 24-cell the characteristic isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. In the skew {30}-gons the chord lengths are:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that visits each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that visits each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that visits each 600-cell vertex once. 

In the 600-cell the characteristic isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. It also takes disjoint 24-cells to each other. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The invariant central planes of this rotation each intersect just one vertex of the 600-cell, which makes two orbits of a great pentagon within the moving invariant plane in the course of one complete isoclinic revolution of period 5. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. 24 Clifford parallel {5/2} pentagram geodesic isoclines of circumference &lt;math&gt;4\pi&lt;/math&gt; over five &lt;math&gt;r_{12}&lt;/math&gt; chords form a circular helix of 24 twisted parallel strands 4{30/12}=24{5/2} that visits each 600-cell vertex once.  


{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <id>2815775</id>
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        <username>Dc.samizdat</username>
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      <text bytes="76299" sha1="cen76hdhmw5r6a1q0866nkwr0b1fqws" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which intersects each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that intersects each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that intersects each 24-cell vertex once. 

In the 24-cell the characteristic isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. In the skew {30}-gons the chord lengths are:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that intersects each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that intersects each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that intersects each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that intersects each 600-cell vertex once. 

In the 600-cell the characteristic isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. It also takes disjoint 24-cells to each other. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The invariant central planes of this rotation each intersect just one vertex of the 600-cell, which makes two orbits of a great pentagon within the moving invariant plane in the course of one complete isoclinic revolution of period 5. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. 24 Clifford parallel {5/2} pentagram geodesic isoclines of circumference &lt;math&gt;4\pi&lt;/math&gt; over five &lt;math&gt;r_{12}&lt;/math&gt; chords form a circular helix of 24 twisted parallel strands 4{30/12}=24{5/2} that intersects each 600-cell vertex once.  


{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <id>2815778</id>
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      <timestamp>2026-06-15T03:40:04Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* Complementary chord pairs and sections */</comment>
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      <text bytes="76332" sha1="2gd2bf2swbx3qp32cd1wzy7e5n6cxfu" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt; based on the polyhedral section. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. 

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
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| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
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|{{radic|2}}
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|- style=&quot;background: seashell;&quot; |
|1.414~
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|1.414~
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|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which intersects each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that intersects each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that intersects each 24-cell vertex once. 

In the 24-cell the characteristic isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. In the skew {30}-gons the chord lengths are:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that intersects each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that intersects each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that intersects each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that intersects each 600-cell vertex once. 

In the 600-cell the characteristic isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. It also takes disjoint 24-cells to each other. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The invariant central planes of this rotation each intersect just one vertex of the 600-cell, which makes two orbits of a great pentagon within the moving invariant plane in the course of one complete isoclinic revolution of period 5. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. 24 Clifford parallel {5/2} pentagram geodesic isoclines of circumference &lt;math&gt;4\pi&lt;/math&gt; over five &lt;math&gt;r_{12}&lt;/math&gt; chords form a circular helix of 24 twisted parallel strands 4{30/12}=24{5/2} that intersects each 600-cell vertex once.  


{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="76332" sha1="8bi5h84rt9lk41okjwcggfa02o0hsud" xml:space="preserve">= Golden chords of the 120-cell =
{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - June 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by 5&lt;sup&gt;2&lt;/sup&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times 5&lt;sup&gt;2&lt;/sup&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains 3&lt;sup&gt;2&lt;/sup&gt; times  5&lt;sup&gt;2&lt;/sup&gt; (225) distinct instances of the 24-point (24-cell), and  3&lt;sup&gt;3&lt;/sup&gt; times 5&lt;sup&gt;2&lt;/sup&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

== Complementary chord pairs and sections ==
The list of 30 chords &lt;math&gt;c_{t}&lt;/math&gt; can be rearranged into a table of 16 rows and 2 columns with a pair of 180° complements in each row. This table first appears in [[w:Regular_Polytopes_(book)|''Regular Polytopes'']] (1947),{{Sfn|Coxeter|1973|loc=Table V(v): Simplified sections of {5,3,3} beginning with a vertex|pp=300-301}} where Coxeter identified each row with a distinct pair of congruent [[w:120-cell#Concentric_hulls|polyhedral sections of the 120-cell]] beginning with a vertex. In spherical [[w:3-sphere|3-dimensional space &lt;math&gt;\mathbb{S}^3&lt;/math&gt;]], every vertex is the center of a set of 29 concentric polyhedra of increasing radii that nest like [[w:Matryoshka_doll|Russian dolls.]] The smallest polyhedral section of radius &lt;math&gt;c_1&lt;/math&gt; is a tetrahedron vertex figure, and the largest section of radius &lt;math&gt;c_{15}&lt;/math&gt; is a central section bisecting the 120-cell[[w:Rhombicosidodecahedron|.]] At radial distances greater than &lt;math&gt;c_{15}&lt;/math&gt; the successive complement-radius polyhedra decrease in size, to the antipodal tetrahedron vertex figure at distance &lt;math&gt;c_{29}&lt;/math&gt;. In Euclidean 4-dimensional space &lt;math&gt;\mathbb{R}^4&lt;/math&gt;, every vertex is the apex of 29 [[w:Hyperpyramid|polyhedral pyramids]] of lateral edge length &lt;math&gt;c_{t}&lt;/math&gt; based on the polyhedral section. Each section lies parallel to a congruent complement-radius section (or coincident with it, in the case of the central section). Each section also lies completely orthogonal to a congruent section. 

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
! colspan=&quot;13&quot; |30 chords (15 180° pairs) make 15 kinds of section polyhedron
|-
! colspan=&quot;5&quot; |Short chord
! 4-polytope
! Polyhedron
! Rectangles
! colspan=&quot;5&quot; |Long chord
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_0&lt;/math&gt;
|0°
|
|
| rowspan=&quot;3&quot; |600 vertices&lt;br&gt;(300 axes)
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_15(2,1).svg|100px|{30/15}=15{2}]]
|180°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{30}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0}}
|
|
|{{radic|4}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0
|
|
|2
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_1&lt;/math&gt;
|15.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_polygon_30.svg|100px|{30/1}]]
| rowspan=&quot;3&quot; |[[File:120-cell_graph_H4.svg|100px|120-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_hexagons_of_the_120-cell.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,7).svg|100px|{30/14}]]
|164.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{29}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.073~}}
|
|
|{{radic|3.927~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.270~
|
|
|1.982~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_2&lt;/math&gt;
|25.2~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,1).svg|100px|{30/2}=2{15}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:25.2°_×_154.8°_chords_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-13.svg|100px|{30/13}]]
|154.8~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{28}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.191~}}
|
|
|{{radic|3.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.437~
|
|
|1.952~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_3&lt;/math&gt;
|36°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,1).svg|100px|{30/3}=3{10}]]
| rowspan=&quot;3&quot; |[[File:600-cell_graph_H4.svg|100px|600-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_decagon_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,2).svg|100px|{30/12}=6{5/2}]]
|144°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{27}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|0.382~}}
|
|
|{{radic|3.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|0.618~
|
|
|1.902~
|
|
|- style=&quot;background: gainsboro;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_4&lt;/math&gt;
|41.4~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:√0.5_×_√3.5_great_rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|138.6~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{26}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.5}}
|
|
|{{radic|3.5}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.707~
|
|
|1.871~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_5&lt;/math&gt;
|44.5~°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,2).svg|100px|{30/4}=2{15/2}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Irregular_great_dodecagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-11.svg|100px|{30/11}]]
|135.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{25}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|0.573~}}
|
|
|{{radic|3.427~}}
|
|
|- style=&quot;background: palegreen;&quot; |
|0.757~
|
|
|1.851~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_6&lt;/math&gt;
|49.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:49.1° × 130.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|130.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{24}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.691~}}
|
|
|{{radic|3.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.831~
|
|
|1.819~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_7&lt;/math&gt;
|56°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:56° × 124° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|124°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{23}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.882~}}
|
|
|{{radic|3.118~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|0.939~
|
|
|1.766~
|
|
|- style=&quot;background: palegreen;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_8&lt;/math&gt;
|60°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_5(6,1).svg|100px|{30/5}=5{6}]]
| rowspan=&quot;3&quot; |[[File:24-cell_t0_F4.svg|100px|24-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_hexagon.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_10(3,1).svg|100px|{30/10}=10{3}]]
|120°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{22}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1}}
|
|
|{{radic|3}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1
|
|
|1.732~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_9&lt;/math&gt;
|66.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:66.1° × 113.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|113.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{21}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.191~}}
|
|
|{{radic|2.809~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.091~
|
|
|1.676~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{10}&lt;/math&gt;
|69.8~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:69.8° × 110.2° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|110.2~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{20}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.309~}}
|
|
|{{radic|2.691~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.144~
|
|
|1.640~
|
|
|- style=&quot;background: yellow;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{11}&lt;/math&gt;
|72°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_6(5,1).svg|100px|{30/6}=6{5}]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_pentagons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_3(10,3).svg|100px|{30/9}=3{10/3}]]
|108°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{19}&lt;/math&gt;
|- style=&quot;background: yellow;&quot; |
|{{radic|1.382~}}
|
|
|{{radic|2.618~}}
|
|
|- style=&quot;background: yellow;&quot; |
|1.176~
|
|
|1.618~
|
|
|- style=&quot;background: palegreen; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{12}&lt;/math&gt;
|75.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:4-simplex_t0.svg|100px|5-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_5-cell_digons_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_figure_2(15,4).svg|100px|{30/8}=2{15/4}]]
|104.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{18}&lt;/math&gt;
|- style=&quot;background: palegreen;&quot; |
|{{radic|1.5}}
|
|
|{{radic|2.5}}
|
|
|- style=&quot;background: palegreen;&quot; |
|1.224~
|
|
|1.581~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{13}&lt;/math&gt;
|81.1~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:81.1° × 98.9° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|98.9~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{17}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|1.691~}}
|
|
|{{radic|2.309~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.300~
|
|
|1.520~
|
|
|- style=&quot;background: gainsboro; height:50px&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{14}&lt;/math&gt;
|84.5~°
|
|
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:84.5° × 95.5° great rectangle.png|100px]]
| rowspan=&quot;3&quot; |
|95.5~°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{16}&lt;/math&gt;
|- style=&quot;background: gainsboro;&quot; |
|{{radic|0.809~}}
|
|
|{{radic|2.191~}}
|
|
|- style=&quot;background: gainsboro;&quot; |
|1.345~
|
|
|1.480~
|
|
|- style=&quot;background: seashell;&quot; |
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|90°
|
|
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
| rowspan=&quot;3&quot; |[[File:4-cube_t3.svg|100px|16-cell]]
| rowspan=&quot;3&quot; |
| rowspan=&quot;3&quot; |[[File:Great_square_rectangle.png|100px]]
| rowspan=&quot;3&quot; |[[File:Regular_star_polygon_30-7.svg|100px|{30/7}]]
|90°
|
|
| rowspan=&quot;3&quot; |&lt;math&gt;c_{15}&lt;/math&gt;
|- style=&quot;background: seashell;&quot; |
|{{radic|2}}
|
|
|{{radic|2}}
|
|
|- style=&quot;background: seashell;&quot; |
|1.414~
|
|
|1.414~
|
|
|}

== The 16-cell 4-orthoplex ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.848,r_3=\sqrt{2}+1 \approx 2.414,r_4=\sqrt{4 + \sqrt{8}} \approx 2.613&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=\sqrt{2}+1&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.414&lt;/math&gt;

Note that &lt;math&gt;r_3-2=1/r_3=\sqrt{2}-1&lt;/math&gt;. The procedure rotates counterclockwise over three &lt;math&gt;r_3&lt;/math&gt; chords of an {8/3} octagram. Over the first &lt;math&gt;r_3&lt;/math&gt; chord the displacement is &lt;math&gt;\sqrt{2}+r_1&lt;/math&gt;. Over the second &lt;math&gt;r_3&lt;/math&gt; chord it moves in the opposite direction a distance of &lt;math&gt;-r_1&lt;/math&gt; . Over the third &lt;math&gt;r_3&lt;/math&gt; chord it moves a distance of &lt;math&gt;-r_1&lt;/math&gt;.

If we embed the planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;math&gt;1/\sqrt{2}&lt;/math&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length and none lie parallel to the projection plane. The octagon circumference is a Petrie polygon. The two disjoint squares lie in completely orthogonal central planes. The blue octagram is a Clifford polygon. ]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt;. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]].{{Efn|name=Petrie polygon of a honeycomb}} The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-[[w:Cross-polytope|orthoplex]], the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;math&gt;\sqrt{2}&lt;/math&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in opposite planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.765,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.848,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

Since the edges of the 16-cell are all the same length &lt;math&gt;r_1=\sqrt{2},r_2=\sqrt{2},r_3=\sqrt{2}&lt;/math&gt;, those chords are distinct only in the context of a rotation. Each chord is a 4-vector with a length and a direction. The rotational curve over each &lt;math&gt;r_i&lt;/math&gt; chord makes &lt;math&gt;i&lt;/math&gt; 45° turns.

[[File:16-cell-orig.gif|thumb|Orthographic projection of the 8-point 16-cell &lt;small&gt;&lt;math&gt;\{3,3,4\}&lt;/math&gt;&lt;/small&gt; performing a double rotation.{{Sfn|Hise|2007}}]]
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a [[W:SO(4)#Double rotations|double rotation]] in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the completely orthogonal planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth, in the left and right rotational directions, between two completely orthogonal great squares formed by &lt;math&gt;r_2&lt;/math&gt; chords.

The &lt;math&gt;r_2&lt;/math&gt; chords of two completely orthogonal great squares lie parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two square central planes rotates that square like a wheel, while the other square does not move.{{Efn|name=simple rotations}} The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in both of two completely orthogonal invariant &lt;math&gt;r_2&lt;/math&gt; square planes at once by equal angles, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The vertex motion is a [[w:Geodesic|geodesic]] circle orbit on the 3-sphere of a special kind: it does not lie in a central plane, its [[w:Winding_number|winding number]] is not 1 (it is 3 in this case), its circumference is not &lt;math&gt;2\pi&lt;/math&gt;, and it moves in either a left or right handed circular spiral. We shall refer to such a chiral circle orbit as an ''isocline'', and to the skew polygram of its rotational chords as a ''Clifford polygon''.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every great square to its completely orthogonal great square in a twisting displacement, as the invariant planes tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once along the same circular helix geodesic isocline of &lt;math&gt;r_3&lt;/math&gt; chords, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. In 360° of isoclinic rotation over four &lt;math&gt;r_3&lt;/math&gt; chords, each vertex makes six 90° turns and reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;6\pi&lt;/math&gt; over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the four &lt;math&gt;r_2&lt;/math&gt; edges of a great square in one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

Because this is the isoclinic rotation of the 16-cell in its invariant edge planes we shall refer to it as the ''characteristic rotation of the 16-cell'', and note once again that it is Fontaine and Hurley's rotation over the &lt;math&gt;r_3&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_3&lt;/math&gt;.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\sqrt{n}&lt;/math&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

[[File:8-cell.gif|thumb|Orthographic projection of the 16-point (8-cell) tesseract &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation about a plane in 4-space.{{Sfn|Hise|2007}} The stationary plane bisects the figure from front-left to back-right and top to bottom.]]
The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] &lt;small&gt;&lt;math&gt;\{4,3,3\}&lt;/math&gt;&lt;/small&gt;. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;math&gt;\sqrt{2}&lt;/math&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The two skew {8/3} octagram Clifford polygons lie on two disjoint parallel isoclines of the same chirality, of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;\sqrt{2}&lt;/math&gt; chords. They form a circular double helix which intersects each vertex of the tesseract once.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes, provided we skewed them both in the same direction. The 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.|name=simple rotations}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
[[File:24-cell vertex geometry.png|thumb|Planar geometry of the radially equilateral 24-cell, showing its 3 great circle polygons and its 4 chord lengths.]]
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 12 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt;. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

[[Image:24-cell.gif|thumb|Orthographic projection of the 24-point 24-cell &lt;small&gt;&lt;math&gt;\{3,4,3\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2007}} The 3-dimensional surface made of 24 octahedra is visible.]]
The 24-cell is [[W:Dual polytope|self-dual]], like the regular polygons and regular simplexes. It is the maximal regular construct of triangles and squares (with no pentagons). It is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;math&gt;\sqrt{3}&lt;/math&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;math&gt;\sqrt{3}&lt;/math&gt; long diameters. The &lt;math&gt;\sqrt{3}&lt;/math&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cell long diameters.

The 24-cell's Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}} \approx 0.518,r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}} \approx 1.932,r_6=\sqrt{4}&lt;/math&gt;

Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that: 

:&lt;math&gt;r_5-r_3+r_1+r_1-r_3=1/r_5&lt;/math&gt;

when &lt;math&gt;r_1=1&lt;/math&gt;. The procedure rotates counterclockwise over five &lt;math&gt;r_5&lt;/math&gt; chords of a {12/5} dodecagram. In the system of unit-radius coordinates &lt;math&gt;r_1=1/r_5&lt;/math&gt;.

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. In the skew dodecagons the chord lengths are:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. Note the {12/5} dodecagram.]]
[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_3=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 24-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The &lt;math&gt;r_3=\sqrt{2}&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Three Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_3&lt;/math&gt; chords form a circular triple helix {24/9}=3{8/3} that intersects each 24-cell vertex once.

[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_5=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 24-cell isoclinically in 4 Clifford parallel invariant great hexagon planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{3}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 24-cell'' in its invariant edge planes, also Fontaine and Hurley's rotation over the &lt;math&gt;r_5&lt;/math&gt; star polygon which constructs &lt;math&gt;1/r_5&lt;/math&gt;. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. The rotational curve over each 120° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Two Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular double helix {24/10}=2{12/5} that intersects each 24-cell vertex once. 

In the 24-cell the characteristic isoclinic rotation by 60° in any invariant hexagon central plane takes every great hexagon to a Clifford parallel great hexagon in a twisting displacement, as all the central planes tilt sideways 60° while rotating 60° internally. It also takes every great square to a Clifford parallel great square in another 16-cell. All 24 vertices move at once on two Clifford parallel geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;10\pi&lt;/math&gt; over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle in the plane twice, over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of a great hexagon in a moving invariant rotation plane. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==
[[Image:600-cell.gif|thumb|Orthographic projection of the 120-point 600-cell &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt; performing a simple rotation.{{Sfn|Hise|2011}} The 3-dimensional surface made of 600 tetrahedra is visible. Invisible in this rendering are 25 inscribed instances of the 24-cell (above), which occur in the 600-cell as interior boundary envelopes.]]
The [[600-cell]] is the regular convex 4-polytope with Schläfli symbol &lt;small&gt;&lt;math&gt;\{3,3,5\}&lt;/math&gt;&lt;/small&gt;. It has 120 vertices, 720 edges, 1200 equilateral triangle faces, and 600 tetrahedron cells. It is the four-dimensional analogue of the icosahedron.

The 600-cell rounds out the 24-cell by adding 96 more vertices between the 24-cell's existing 24 vertices, in effect adding twenty-four more 24-cells inscribed in the 600-cell. The new surface thus formed is a honeycomb of smaller, more numerous cells: tetrahedra of edge length &lt;math&gt;\phi^{-1} \approx 0.618&lt;/math&gt; instead of octahedra of edge length &lt;math&gt;\sqrt{1}&lt;/math&gt;. It encloses the &lt;math&gt;\sqrt{1}&lt;/math&gt; edges of the 24-cells, which become invisible interior chords in the 600-cell, like the &lt;math&gt;\sqrt{2}&lt;/math&gt; and &lt;math&gt;\sqrt{3}&lt;/math&gt; chords.

Since the tetrahedra are made of shorter triangle edges than the octahedra (by a factor of &lt;math&gt;\phi^{-1}&lt;/math&gt;, the inverse golden ratio), the 600-cell is not radially equilateral like the 24-cell and the tesseract. Like them it is radially triangular in a special way, but one in which [[w:Golden_triangle_(mathematics)|golden triangles]] rather than equilateral triangles meet at the center.

In 2-space we have the ''radially golden'' [[W:Decagon#The golden ratio in decagon|regular decagon]]. In 3-space we have the radially golden 30-point [[W:icosidodecahedron|icosidodecahedron]], with 6 decagon central planes. In 4-space we have the radially golden 120-point 600-cell, with 60 icosidodecahedron central hyperplanes and 72 decagon central planes.

The 600-cell's Petrie polygon is the regular [[w:Triacontagon|triacontagon {30}]]. The unit-radius planar {30}-gon has these distinct chords:

:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{15}/2) \approx 0.209&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{2\pi}{15}/2) \approx 0.416&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{4\pi}{15}/2) \approx 0.813&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{7\pi}{15}/2) \approx 1.338&lt;/math&gt;
:&lt;math&gt;r_8=2 \cos (\tfrac{7\pi}{15}/2) \approx 1.486&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \cos (\tfrac{4\pi}{15}/2) \approx 1.827&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \cos (\tfrac{2\pi}{15}/2) \approx 1.956&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \cos (\tfrac{\pi}{15}/2) \approx 1.989&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Only the chord lengths &lt;math&gt;r_3&lt;/math&gt;, &lt;math&gt;r_5&lt;/math&gt;, &lt;math&gt;r_6&lt;/math&gt;, &lt;math&gt;\sqrt{2}&lt;/math&gt;, &lt;math&gt;r_9&lt;/math&gt;, &lt;math&gt;r_{10}&lt;/math&gt;, &lt;math&gt;r_{12}&lt;/math&gt;, &lt;math&gt;r_{15}&lt;/math&gt; occur in the 600-cell, which is a construct of 24 Petrie {30}-gons of edge length &lt;math&gt;r_3&lt;/math&gt;, six of which intersect in each icosahedral vertex figure. In the skew {30}-gons the chord lengths are:

[[File:600-cell vertex geometry.png|thumb|Planar geometry of the 600-cell, showing its 5 regular great circle polygons and its 8 chord lengths with angles of arc. The golden ratio governs the fractional roots of every other chord, and the radial golden triangles which meet at the center.|400x400px]]
:&lt;math&gt;r_1=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_2=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_3=2 \sin (\tfrac{\pi}{5}/2)=1/\phi \approx 0.618&lt;/math&gt;
:&lt;math&gt;r_4=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}&lt;/math&gt;
:&lt;math&gt;r_5=2 \sin (\tfrac{\pi}{3}/2)=\sqrt{1}=\text{24-cell-}r_2&lt;/math&gt;
:&lt;math&gt;r_6=2 \sin (\tfrac{2\pi}{5}/2)=\sqrt{3-\phi} \approx 1.176&lt;/math&gt;
:&lt;math&gt;r_7=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}&lt;/math&gt;
:&lt;math&gt;r_8=2 \sin (\tfrac{\pi}{2}/2)=\sqrt{2}=\text{16-cell-}r_3&lt;/math&gt;
:&lt;math&gt;r_9=2 \sin (\tfrac{3\pi}{5}/2)=\phi \approx 1.618&lt;/math&gt;
:&lt;math&gt;r_{10}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}=\text{24-cell-}r_5&lt;/math&gt;
:&lt;math&gt;r_{11}=2 \sin (\tfrac{2\pi}{3}/2)=\sqrt{3}&lt;/math&gt;
:&lt;math&gt;r_{12}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{13}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{14}=2 \sin (\tfrac{4\pi}{5}/2)=\sqrt{2+\phi} \approx 1.902&lt;/math&gt;
:&lt;math&gt;r_{15}=2 \sin (\pi/2)=\sqrt{4}&lt;/math&gt;

Where chords are the same length, they are distinct only in the context of a rotation.

[[File:Regular_star_figure_3(8,3).svg|thumb|left|150px|{24/9}=3{8/3} &lt;small&gt;&lt;math&gt;r_8=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
We can rotate the 600-cell isoclinically in the characteristic rotation of the 16-cell, by 90° in two completely orthogonal invariant great square planes over &lt;math&gt;r_8=\sqrt{2}&lt;/math&gt; isocline chords, with the same effect on 15 disjoint 16-cells. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_8&lt;/math&gt; chord is the 16-cell &lt;math&gt;r_3&lt;/math&gt; chord. The rotational curve over each 90° &lt;math&gt;r_3&lt;/math&gt; chord makes three 45° turns. Fifteen Clifford parallel {8/3} octagram geodesic isoclines of circumference &lt;math&gt;6\pi&lt;/math&gt; over &lt;math&gt;r_8&lt;/math&gt; chords form a circular helix of 15 twisted parallel strands 5{24/9}=15{8/3} that intersects each 600-cell vertex once.

{{Clear}}
[[File:Regular_star_polygon_30-7.svg|thumb|left|150px|{30/7} &lt;small&gt;&lt;math&gt;r_7=\sqrt{2}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct 90° isoclinic rotation, over &lt;math&gt;r_7=\sqrt{2}&lt;/math&gt; isocline chords. This rotation has period 30 and visits every vertex of a 600-cell Petrie polygon. Each 90° isoclinic rotational displacement takes every great square plane to a great square plane in another 16-cell. The invariant completely orthogonal central planes of this rotation each intersect only one vertex of the 600-cell, which makes seven orbits on a great circle within the moving invariant plane in the course of one complete isoclinic revolution. The rotational curve over each 90° &lt;math&gt;r_7&lt;/math&gt; isocline chord makes seven 12° turns. Four Clifford parallel {30/7} geodesic isoclines of circumference &lt;math&gt;14\pi&lt;/math&gt; over &lt;math&gt;r_7&lt;/math&gt; chords form a circular quadruple helix that intersects each 600-cell vertex once.

{{Clear}}
[[File:Regular star figure 2(12,5).svg|thumb|left|150px|{24/10}=2{12/5} &lt;small&gt;&lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt;&lt;/small&gt; ]]
We can also rotate the 600-cell isoclinically  in the characteristic rotation of the 24-cell, by 60° in great hexagon planes over &lt;math&gt;r_{10}=\sqrt{3}&lt;/math&gt; isocline chords, with the same effect on 5 disjoint 24-cells. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions of its 24-cell just once and returns to its original position, without visiting other vertex positions. The &lt;math&gt;r_{10}&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_5&lt;/math&gt; chord. The rotational curve over each 60° &lt;math&gt;r_5&lt;/math&gt; chord makes five 30° turns. Ten Clifford parallel {12/5} dodecagram geodesic isoclines of circumference &lt;math&gt;10\pi&lt;/math&gt; over &lt;math&gt;r_{10}&lt;/math&gt; chords form a circular helix of 10 twisted parallel strands 5{24/10}=10{12/5} that intersects each 600-cell vertex once. 

{{Clear}}
[[File:Regular_star_figure_2(15,4).svg|thumb|left|150px|{30/8}=2{15/4} &lt;small&gt;&lt;math&gt;r_5=\sqrt{1}&lt;/math&gt;&lt;/small&gt;]]
We can also rotate the 600-cell isoclinically in 12 Clifford parallel invariant decagon central planes containing its vertices, over &lt;math&gt;r_{5}=\sqrt{1}&lt;/math&gt; isocline chords. This is the ''characteristic rotation of the 600-cell'' in its invariant edge planes. Its Clifford polygon is a skew {15/4} pentadecagram of &lt;math&gt;r_5&lt;/math&gt; chords. The &lt;math&gt;r_5&lt;/math&gt; chord is the 24-cell &lt;math&gt;r_2&lt;/math&gt; chord. Successive &lt;math&gt;r_5&lt;/math&gt; chords are edges of different 24-cells. The rotational curve over each &lt;math&gt;r_5&lt;/math&gt; chord makes five 12° turns. Eight Clifford parallel {15/4} pentadecagon geodesic isoclines of circumference &lt;math&gt;5\pi&lt;/math&gt; over &lt;math&gt;r_5&lt;/math&gt; chords form a circular helix of eight twisted parallel strands 4{30/8}=8{15/4} that intersects each 600-cell vertex once. 

In the 600-cell the characteristic isoclinic rotation by 36° in any invariant decagon central plane takes every great decagon to a Clifford parallel great decagon in a twisting displacement, as all the central planes tilt sideways 36° while rotating 36° internally. It also takes every great hexagon to a Clifford parallel great hexagon in another 24-cell, and every great square to a Clifford parallel great square in another 16-cell. All 120 vertices move at once on eight Clifford parallel geodesic isoclines, displaced 60° in different directions.

The trajectory of each vertex over each 36° isoclinic rotational displacement is a one-fifteenth segment of its geodesic orbit. Its entire orbit traces an isocline circle in 4-space of circumference &lt;math&gt;5\pi&lt;/math&gt; over 15 &lt;math&gt;r_5&lt;/math&gt; chords, and also traces an ordinary great circle in the plane 3 times, over the 5 edges of a great pentagon in a moving invariant rotation plane. In the course of a complete isoclinic revolution each vertex departs from 15 vertex positions just once and returns to its original position, and the 600-cell returns to its original orientation.

{{Clear}}
[[File:Regular_star_figure_6(5,2).svg|thumb|left|150px|{30/12}=6{5/2} &lt;small&gt;&lt;math&gt;r_{12}=\sqrt{2+\phi}&lt;/math&gt;&lt;/small&gt;]]
In the 600-cell there is another distinct isoclinic rotation taking decagon planes to each other, over 144° &lt;math&gt;r_{12}&lt;/math&gt; isocline chords. It also takes disjoint 24-cells to each other. This rotation has period 5 and visits every 12th vertex of a 600-cell Petrie polygon. Its Clifford polygon is a skew {5/2} pentagram of &lt;math&gt;r_{12}&lt;/math&gt; chords. The invariant central planes of this rotation each intersect only one vertex of the 600-cell, which makes two orbits of a great pentagon within the moving invariant plane in the course of one complete isoclinic revolution of period 5. The rotational curve over each &lt;math&gt;r_{12}&lt;/math&gt; chord makes twelve 12° turns. 24 Clifford parallel {5/2} pentagram geodesic isoclines of circumference &lt;math&gt;4\pi&lt;/math&gt; over five &lt;math&gt;r_{12}&lt;/math&gt; chords form a circular helix of 24 twisted parallel strands 4{30/12}=24{5/2} that intersects each 600-cell vertex once.  


{{Clear}}

== The 5-cell 4-simplex ==
In [[User:Dc.samizdat/Golden chords of the 120-cell#Complementary chord pairs|the table above]] Coxeter showed that the 120-cell has 30 distinct chords in 180° complementary pairs. Only 8 of those 30 chords occur in the 600-cell and the planar {30)-gon. The 120-cell's additional chords arise originally from the regular 5-cell, in its interaction with the other regular 4-polytopes that compound to make the 120-cell. All those polytopes except the 5-cell occur in the 600-cell. Since the 120-cell and the 600-cell have the same symmetry group, the 5-cell's symmetry group is what's new in the 120-cell. 

...

== Finally the 120-cell ==
The 120-cell is the [[W:Dual polytope|dual polytope]] of the 600-cell. They have the same Petrie polygon, the regular skew triacontagon {30}, but the 120-cell is a construct of 40 Petrie {30}-gons of edge length &lt;math&gt;c_1&lt;/math&gt;, two of which intersect in each tetrahedral vertex figure. 

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a geometric formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the characteristic isoclinic rotation of a ''d''-dimensional polytope in its invariant edge planes. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords. [If what is meant by this is its Petrie polygon, it is not quite necessary or possible with respect to the planar polygon chords, e.g. the planar Petrie polygon of the 600-cell does not contain the &lt;math&gt;\sqrt{2}&lt;/math&gt; chord. But perhaps it would work if the fit is to the smallest regular skew polygon in the ''d''-space.]

The discovery of a chordal construction for discrete isoclinic rotations generally closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in the 120-cell demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden chord sequences in polygons, to sequences of star polygons in isoclinic rotations, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

== Appendix: Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>8bi5h84rt9lk41okjwcggfa02o0hsud</sha1>
    </revision>
  </page>
  <page>
    <title>Talk:WikiJournal Preprints/Pentagram map</title>
    <ns>1</ns>
    <id>326949</id>
    <revision>
      <id>2815748</id>
      <parentid>2812589</parentid>
      <timestamp>2026-06-15T02:30:39Z</timestamp>
      <contributor>
        <username>OhanaUnited</username>
        <id>18921</id>
      </contributor>
      <comment>/* Peer review 2 */ new section</comment>
      <origin>2815748</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10264" sha1="jbcy8t47zz4vbthw6nq8c8j3i9tvrv1" xml:space="preserve">== Slight modifications of the article ==

Hello,&lt;br&gt;
I imported this page from the Wikipedia article, which I revamped. But since the import, some contributors made helpful comments and edits. I tried to update them all here, but now I stopped and I will just re-import the Wikipedia article when the peer-review process will start. Please notify me when it happens, or re-import it yourself {{=)}}. [[User:Regliste|Regliste]] ([[User talk:Regliste|discuss]] • [[Special:Contributions/Regliste|contribs]]) 09:48, 13 January 2026 (UTC)

==Peer review 1==
{{review
 |reviewer   =Sanjay Ramassamy
 |Q          =Q102641962
 |affiliation=Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique
 |link       =https://www.normalesup.org/~ramassamy/index.html.en
 |date       = 1 June 2026
 |text       =
This review article is very well-written, mathematically sound and accessible to people outside the field. I only have minor comments below, most of them typos. I recommend publishing the article once the comments are taken into account.

General comment: There are several figures next to the text, but the figures don't seem to be cited in the text. I don't know if this is a journal policy, but it looks a bit unusual to me.

Second sentence of the abstract: there is twice &quot;&quot;a new polygon&quot;&quot;. Maybe you could rephrase it in a way to eliminate one of the occurrences. E.g. something like &quot;&quot;It defines a new polygon whose vertices are obtained as the intersection points of the shortest diagonals of the initial polygon.&quot;&quot;

End of first paragraph of the abstract: maybe you could already reference Schwartz's original paper here.

Euclidean plane: please capitalize the first letter of &quot;&quot;Euclidean&quot;&quot; throughout the article

Section &quot;&quot;On polygons&quot;&quot;: &quot;&quot;Finally, it is possible that two diagonals are parallel and not intersect&quot;&quot; -&gt; &quot;&quot;and don't intersect&quot;&quot;

Section &quot;&quot;On the moduli space of polygons&quot;&quot;: it is the first time that I see the term &quot;&quot;projectivity&quot;&quot;. I checked that it was indeed correct, but in all the talks/articles that I have seen on the topic, people rather used &quot;&quot;up to projective transformations&quot;&quot;.

Section &quot;&quot;Historical elements&quot;&quot;, last sentence: it is not too clear what that sentence means. The pentagram map pertains to the field of incidence geometry, like these 3 theorems. What are the further similarities ? Further down in the article, in the section &quot;&quot;Pentagons and hexagons&quot;&quot;, there is a similar sentence: &quot;&quot;The action of the pentagram map on pentagons and hexagons is similar in spirit to classical configuration theorems in projective geometry such as Pascal's theorem, Desargues's theorem and others&quot;&quot;. Is it just the case of pentagons and hexagons that resembles these theorems ?

Section &quot;&quot;Definition of the map&quot;&quot;, first paragraph: it looks strange to cite Weinreich's paper to justify the rather obvious fact that the dimension of the space of n-gons is 2n. More generally, for review articles in WikiJournal, what is the purpose of citations ? Providing a source where something is nicely explained ? Or providing the first source to show some result ? In this article, it seems to be rather the former.

Section &quot;&quot;Definition of the map&quot;&quot;, second paragraph: &quot;&quot;Taking the intersection of the two...&quot;&quot; -&gt; &quot;&quot;Taking the intersection of two...&quot;&quot;

Section &quot;&quot;Twisted polygons&quot;&quot;: &quot;&quot;space of twisted n-gon&quot;&quot; -&gt; &quot;&quot;space of twisted n-gons&quot;&quot;

&quot;&quot;the dynamic&quot;&quot; -&gt; &quot;&quot;the dynamics&quot;&quot; It comes with a final s even though it is singular, e.g. &quot;&quot;the dynamics is integrable&quot;&quot;

Section &quot;&quot;Pentagons and hexagons&quot;&quot;: &quot;&quot;The two following facts&quot;&quot; -&gt; &quot;&quot;The following two facts&quot;&quot;

Section &quot;&quot;Poncelet polygons&quot;&quot;: circumbscribed -&gt; circumscribed

Section &quot;&quot;Poncelet polygons&quot;&quot;: &quot;&quot;For a convex Poncelet n-gons&quot;&quot; -&gt; n-gon

Section &quot;&quot;ab-coordinates&quot;&quot;: I would write &quot;&quot;vertices v_k&quot;&quot; and &quot;&quot;vectors V_k&quot;&quot; rather than &quot;&quot;vertices v_k's&quot;&quot; and &quot;&quot;vectors V_k's&quot;&quot;

Section &quot;&quot;As a birational map&quot;&quot;: you have twice in a row the word pentagram in the first line

Section &quot;&quot;The scaling symmetry&quot;&quot;: &quot;&quot;an s&quot;&quot; -&gt; &quot;&quot;and s&quot;&quot;. 

Section &quot;&quot;The scaling symmetry&quot;&quot;: &quot;&quot;An homogeneous&quot;&quot; -&gt; &quot;&quot;A homogeneous&quot;&quot;. Why do you define the notion of weight in this section ? It looks weird because you don't use it immediately, but only towards the end of the next section. It would suggest moving it much closer to the place where you first use it.

Section &quot;&quot;The spectral curve&quot;&quot;, last sentence: here you write &quot;&quot;algebraic integrability&quot;&quot;. In the next sentence it is called &quot;&quot;algebro-geometric integrability&quot;&quot;. I prefer the latter formulation.

Section &quot;&quot;The spectral curve&quot;&quot;: &quot;&quot;some renormalization it&quot;&quot; -&gt; missing &quot;&quot;of&quot;&quot;

Section &quot;&quot;Algebro-geometric integrability&quot;&quot;: &quot;&quot;in term of&quot;&quot; -&gt; terms

Section &quot;&quot;Dimension of the invariant manifold&quot;&quot;: &quot;&quot;For a twisted n-gons&quot;&quot; -&gt; &quot;&quot;For twisted n-gons&quot;&quot;

Section &quot;&quot;Dimension of the invariant manifold&quot;&quot;: what does it mean that the dimension of the invariant tori drops by 3 for closed n-gons ? That it is always n-3 regardless of the parity of n ? Shouldn't invariant tori always be even-dimensional ? Maybe make a separate sentence discussing the closed n-gons case.

Section &quot;&quot;Cluster algebras&quot;&quot;: rather than &quot;&quot;special cases of cluster algebra&quot;&quot;, I would suggest something like &quot;&quot;special cases of discrete dynamical systems powered by cluster algebras&quot;&quot;. Because the pentagram map itself is not a cluster algebra. Also, the mutations of the underlying cluster algebra induced by the pentagram map are only a subset of all possible mutations.

Section &quot;&quot;Generalizations&quot;&quot;: &quot;&quot;description ... as cluster algebras&quot;&quot; -&gt; maybe &quot;&quot;in terms of cluster algebras&quot;&quot; ?

Section &quot;&quot;Generalized pentagram maps&quot;&quot;: it could be helpful to write that one recovers the original pentagram map by taking d=2, I={2}, J={1}. What surprises me is that for this original pentagram map the set I and J are not equal and yet it is integrable. How is that compatible with the statement that &quot;&quot;the general case is not integrable&quot;&quot; ? Also, just below, the dented pentagram maps provide another class of integrable examples where I and J are not equal. How do you quantify that most cases are not integrable.

Section &quot;&quot;Corrugated polygons&quot;&quot;: &quot;&quot;they can retrieved&quot;&quot; -&gt; &quot;&quot;they can be retrieved&quot;&quot;

&quot;&quot;Grassmannians polygons&quot;&quot; -&gt; &quot;&quot;Grassmannian polygons&quot;&quot;

&quot;&quot;the space of Grassmannians Gr(m,md)&quot;&quot; -&gt; &quot;&quot;the Grassmannian space Gr(m,md)&quot;&quot;

&quot;&quot;A point in v&quot;&quot; -&gt; &quot;&quot;A point v&quot;&quot;

&quot;&quot;general linear group Gl_{md}&quot;&quot; -&gt; &quot;&quot;general linear group GL_{md}&quot;&quot;

&quot;&quot;faithfull&quot;&quot; -&gt; faithful

&quot;&quot;generically define&quot;&quot; -&gt; &quot;&quot;generically defines&quot;&quot;

&quot;&quot;a new point of v&quot;&quot; -&gt; &quot;&quot;a new point v&quot;&quot;

}}

{{response|1 =Hello, and thanks a lot for the thorough review. I am a bit embarrassed by the numerous typos, they are now fixed. I also reformulated many items following your suggestions. There remains two points I need to answer to.
* Indeed, the citation of papers (even for obvious facts) is more frequent than in classical papers. This is because Wikipedia aims to have every statement linked to a reference (see [[w:Wikipedia:Verifiability]]). Some editors take this very seriously (see [https://en.wikipedia.org/wiki/Wikipedia%20talk:WikiProject%20Mathematics/Archive/2025/Dec this discussion]), so I added citations to almost every paragraphs. I guess it could be mitigated for publication.
* I clarified the statement about the dimension of invariant manifolds for closed polygons, with one more citation. According to it, they will always be odd-dimensional.
Thanks again, [[User:Regliste|Regliste]] ([[User talk:Regliste|discuss]] • [[Special:Contributions/Regliste|contribs]]) 15:44, 2 June 2026 (UTC)}}

== Peer review 2 ==

{{review
 |reviewer   =Paul Melotti
 |Q          =
 |affiliation=Université Paris-Saclay
 |link       =https://www.imo.universite-paris-saclay.fr/~paul.melotti/
 |date       = 11 June 2026
 |text       =
This is a very well-written summary of results on the pentagram map, a fascinating topic that deserved a good presentation in the wikipedia universe. The paper is presented in a clear and coherent way, and I believe it is accessible to non-specialists, provided some minimal background in projective geometry. As far as I could check, the claims are supported by the plentiful references, and they give a good overview of the topic, its history, connections to various topics in mathematics, and modern perspectives.

As a general remark, I think the special property of the map T on the spaces of pentagons and hexagons, stated in Section &quot;Periodic orbits on the moduli space&quot;, could be stated earlier in the paper, possibly in an informal way. They are quite striking and, in my opinion, motivate the study of the generic transformation.

Here are a few minor remarks:
- several references to pictures use the phrase &quot;on Figure...&quot;, I believe &quot;in Figure...&quot; is more common.
- &quot;its interpretation as a cluster algebra&quot; -&gt; maybe &quot;in terms of a cluster algebra&quot;, or something similar, would be more precise.
- On reference [2] by Gekhtman and Izosimov, &quot;Integrable Systems and Cluster Algebras&quot;, the link to sciencedirect in &quot;Works cited&quot; doesn't seem to work when I click it. This might be on my side, but please check the URL.
- &quot;for generic polygons on the real projective plane&quot; -&gt; &quot;in&quot; the projective plane seems more common?
- &quot;by taking lines and intersections of them&quot; sound a bit weird to me (but I'm not a native speaker so maybe it's okay)
- maybe at the beginning of Section &quot;Coordinates for the moduli space&quot;, announce that these will allow for nice expressions of the map T in those coordinates (as it is done in the following section).
- &quot;This generically makes a quasiperiodic motion.&quot; -&gt; &quot;makes&quot; sounds a bit vague to me, maybe &quot;induces a quasiperiodic motion on the corresponding torus&quot; or something.
- In the subsection &quot;Grassmannian polygon&quot;, second paragraph, I am a bit confused with notations and conventions. If we represent the vector space $v$ by a basis, and put the vectors in columns, we get a matrix of size $md \times m$ and not $m \times md$ right? And then, the action of $GL_{md}$ you are mentioning is simply multiplication on the left?
}} [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 02:30, 15 June 2026 (UTC)</text>
      <sha1>jbcy8t47zz4vbthw6nq8c8j3i9tvrv1</sha1>
    </revision>
    <revision>
      <id>2815749</id>
      <parentid>2815748</parentid>
      <timestamp>2026-06-15T02:31:25Z</timestamp>
      <contributor>
        <username>OhanaUnited</username>
        <id>18921</id>
      </contributor>
      <comment>/* Peer review 2 */ Q id</comment>
      <origin>2815749</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10275" sha1="6mf2cq1p5pjnkreuek8fd27vopsygef" xml:space="preserve">== Slight modifications of the article ==

Hello,&lt;br&gt;
I imported this page from the Wikipedia article, which I revamped. But since the import, some contributors made helpful comments and edits. I tried to update them all here, but now I stopped and I will just re-import the Wikipedia article when the peer-review process will start. Please notify me when it happens, or re-import it yourself {{=)}}. [[User:Regliste|Regliste]] ([[User talk:Regliste|discuss]] • [[Special:Contributions/Regliste|contribs]]) 09:48, 13 January 2026 (UTC)

==Peer review 1==
{{review
 |reviewer   =Sanjay Ramassamy
 |Q          =Q102641962
 |affiliation=Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique
 |link       =https://www.normalesup.org/~ramassamy/index.html.en
 |date       = 1 June 2026
 |text       =
This review article is very well-written, mathematically sound and accessible to people outside the field. I only have minor comments below, most of them typos. I recommend publishing the article once the comments are taken into account.

General comment: There are several figures next to the text, but the figures don't seem to be cited in the text. I don't know if this is a journal policy, but it looks a bit unusual to me.

Second sentence of the abstract: there is twice &quot;&quot;a new polygon&quot;&quot;. Maybe you could rephrase it in a way to eliminate one of the occurrences. E.g. something like &quot;&quot;It defines a new polygon whose vertices are obtained as the intersection points of the shortest diagonals of the initial polygon.&quot;&quot;

End of first paragraph of the abstract: maybe you could already reference Schwartz's original paper here.

Euclidean plane: please capitalize the first letter of &quot;&quot;Euclidean&quot;&quot; throughout the article

Section &quot;&quot;On polygons&quot;&quot;: &quot;&quot;Finally, it is possible that two diagonals are parallel and not intersect&quot;&quot; -&gt; &quot;&quot;and don't intersect&quot;&quot;

Section &quot;&quot;On the moduli space of polygons&quot;&quot;: it is the first time that I see the term &quot;&quot;projectivity&quot;&quot;. I checked that it was indeed correct, but in all the talks/articles that I have seen on the topic, people rather used &quot;&quot;up to projective transformations&quot;&quot;.

Section &quot;&quot;Historical elements&quot;&quot;, last sentence: it is not too clear what that sentence means. The pentagram map pertains to the field of incidence geometry, like these 3 theorems. What are the further similarities ? Further down in the article, in the section &quot;&quot;Pentagons and hexagons&quot;&quot;, there is a similar sentence: &quot;&quot;The action of the pentagram map on pentagons and hexagons is similar in spirit to classical configuration theorems in projective geometry such as Pascal's theorem, Desargues's theorem and others&quot;&quot;. Is it just the case of pentagons and hexagons that resembles these theorems ?

Section &quot;&quot;Definition of the map&quot;&quot;, first paragraph: it looks strange to cite Weinreich's paper to justify the rather obvious fact that the dimension of the space of n-gons is 2n. More generally, for review articles in WikiJournal, what is the purpose of citations ? Providing a source where something is nicely explained ? Or providing the first source to show some result ? In this article, it seems to be rather the former.

Section &quot;&quot;Definition of the map&quot;&quot;, second paragraph: &quot;&quot;Taking the intersection of the two...&quot;&quot; -&gt; &quot;&quot;Taking the intersection of two...&quot;&quot;

Section &quot;&quot;Twisted polygons&quot;&quot;: &quot;&quot;space of twisted n-gon&quot;&quot; -&gt; &quot;&quot;space of twisted n-gons&quot;&quot;

&quot;&quot;the dynamic&quot;&quot; -&gt; &quot;&quot;the dynamics&quot;&quot; It comes with a final s even though it is singular, e.g. &quot;&quot;the dynamics is integrable&quot;&quot;

Section &quot;&quot;Pentagons and hexagons&quot;&quot;: &quot;&quot;The two following facts&quot;&quot; -&gt; &quot;&quot;The following two facts&quot;&quot;

Section &quot;&quot;Poncelet polygons&quot;&quot;: circumbscribed -&gt; circumscribed

Section &quot;&quot;Poncelet polygons&quot;&quot;: &quot;&quot;For a convex Poncelet n-gons&quot;&quot; -&gt; n-gon

Section &quot;&quot;ab-coordinates&quot;&quot;: I would write &quot;&quot;vertices v_k&quot;&quot; and &quot;&quot;vectors V_k&quot;&quot; rather than &quot;&quot;vertices v_k's&quot;&quot; and &quot;&quot;vectors V_k's&quot;&quot;

Section &quot;&quot;As a birational map&quot;&quot;: you have twice in a row the word pentagram in the first line

Section &quot;&quot;The scaling symmetry&quot;&quot;: &quot;&quot;an s&quot;&quot; -&gt; &quot;&quot;and s&quot;&quot;. 

Section &quot;&quot;The scaling symmetry&quot;&quot;: &quot;&quot;An homogeneous&quot;&quot; -&gt; &quot;&quot;A homogeneous&quot;&quot;. Why do you define the notion of weight in this section ? It looks weird because you don't use it immediately, but only towards the end of the next section. It would suggest moving it much closer to the place where you first use it.

Section &quot;&quot;The spectral curve&quot;&quot;, last sentence: here you write &quot;&quot;algebraic integrability&quot;&quot;. In the next sentence it is called &quot;&quot;algebro-geometric integrability&quot;&quot;. I prefer the latter formulation.

Section &quot;&quot;The spectral curve&quot;&quot;: &quot;&quot;some renormalization it&quot;&quot; -&gt; missing &quot;&quot;of&quot;&quot;

Section &quot;&quot;Algebro-geometric integrability&quot;&quot;: &quot;&quot;in term of&quot;&quot; -&gt; terms

Section &quot;&quot;Dimension of the invariant manifold&quot;&quot;: &quot;&quot;For a twisted n-gons&quot;&quot; -&gt; &quot;&quot;For twisted n-gons&quot;&quot;

Section &quot;&quot;Dimension of the invariant manifold&quot;&quot;: what does it mean that the dimension of the invariant tori drops by 3 for closed n-gons ? That it is always n-3 regardless of the parity of n ? Shouldn't invariant tori always be even-dimensional ? Maybe make a separate sentence discussing the closed n-gons case.

Section &quot;&quot;Cluster algebras&quot;&quot;: rather than &quot;&quot;special cases of cluster algebra&quot;&quot;, I would suggest something like &quot;&quot;special cases of discrete dynamical systems powered by cluster algebras&quot;&quot;. Because the pentagram map itself is not a cluster algebra. Also, the mutations of the underlying cluster algebra induced by the pentagram map are only a subset of all possible mutations.

Section &quot;&quot;Generalizations&quot;&quot;: &quot;&quot;description ... as cluster algebras&quot;&quot; -&gt; maybe &quot;&quot;in terms of cluster algebras&quot;&quot; ?

Section &quot;&quot;Generalized pentagram maps&quot;&quot;: it could be helpful to write that one recovers the original pentagram map by taking d=2, I={2}, J={1}. What surprises me is that for this original pentagram map the set I and J are not equal and yet it is integrable. How is that compatible with the statement that &quot;&quot;the general case is not integrable&quot;&quot; ? Also, just below, the dented pentagram maps provide another class of integrable examples where I and J are not equal. How do you quantify that most cases are not integrable.

Section &quot;&quot;Corrugated polygons&quot;&quot;: &quot;&quot;they can retrieved&quot;&quot; -&gt; &quot;&quot;they can be retrieved&quot;&quot;

&quot;&quot;Grassmannians polygons&quot;&quot; -&gt; &quot;&quot;Grassmannian polygons&quot;&quot;

&quot;&quot;the space of Grassmannians Gr(m,md)&quot;&quot; -&gt; &quot;&quot;the Grassmannian space Gr(m,md)&quot;&quot;

&quot;&quot;A point in v&quot;&quot; -&gt; &quot;&quot;A point v&quot;&quot;

&quot;&quot;general linear group Gl_{md}&quot;&quot; -&gt; &quot;&quot;general linear group GL_{md}&quot;&quot;

&quot;&quot;faithfull&quot;&quot; -&gt; faithful

&quot;&quot;generically define&quot;&quot; -&gt; &quot;&quot;generically defines&quot;&quot;

&quot;&quot;a new point of v&quot;&quot; -&gt; &quot;&quot;a new point v&quot;&quot;

}}

{{response|1 =Hello, and thanks a lot for the thorough review. I am a bit embarrassed by the numerous typos, they are now fixed. I also reformulated many items following your suggestions. There remains two points I need to answer to.
* Indeed, the citation of papers (even for obvious facts) is more frequent than in classical papers. This is because Wikipedia aims to have every statement linked to a reference (see [[w:Wikipedia:Verifiability]]). Some editors take this very seriously (see [https://en.wikipedia.org/wiki/Wikipedia%20talk:WikiProject%20Mathematics/Archive/2025/Dec this discussion]), so I added citations to almost every paragraphs. I guess it could be mitigated for publication.
* I clarified the statement about the dimension of invariant manifolds for closed polygons, with one more citation. According to it, they will always be odd-dimensional.
Thanks again, [[User:Regliste|Regliste]] ([[User talk:Regliste|discuss]] • [[Special:Contributions/Regliste|contribs]]) 15:44, 2 June 2026 (UTC)}}

== Peer review 2 ==

{{review
 |reviewer   =Paul Melotti
 |Q          = Q103240269
 |affiliation=Université Paris-Saclay
 |link       =https://www.imo.universite-paris-saclay.fr/~paul.melotti/
 |date       = 11 June 2026
 |text       =
This is a very well-written summary of results on the pentagram map, a fascinating topic that deserved a good presentation in the wikipedia universe. The paper is presented in a clear and coherent way, and I believe it is accessible to non-specialists, provided some minimal background in projective geometry. As far as I could check, the claims are supported by the plentiful references, and they give a good overview of the topic, its history, connections to various topics in mathematics, and modern perspectives.

As a general remark, I think the special property of the map T on the spaces of pentagons and hexagons, stated in Section &quot;Periodic orbits on the moduli space&quot;, could be stated earlier in the paper, possibly in an informal way. They are quite striking and, in my opinion, motivate the study of the generic transformation.

Here are a few minor remarks:
- several references to pictures use the phrase &quot;on Figure...&quot;, I believe &quot;in Figure...&quot; is more common.
- &quot;its interpretation as a cluster algebra&quot; -&gt; maybe &quot;in terms of a cluster algebra&quot;, or something similar, would be more precise.
- On reference [2] by Gekhtman and Izosimov, &quot;Integrable Systems and Cluster Algebras&quot;, the link to sciencedirect in &quot;Works cited&quot; doesn't seem to work when I click it. This might be on my side, but please check the URL.
- &quot;for generic polygons on the real projective plane&quot; -&gt; &quot;in&quot; the projective plane seems more common?
- &quot;by taking lines and intersections of them&quot; sound a bit weird to me (but I'm not a native speaker so maybe it's okay)
- maybe at the beginning of Section &quot;Coordinates for the moduli space&quot;, announce that these will allow for nice expressions of the map T in those coordinates (as it is done in the following section).
- &quot;This generically makes a quasiperiodic motion.&quot; -&gt; &quot;makes&quot; sounds a bit vague to me, maybe &quot;induces a quasiperiodic motion on the corresponding torus&quot; or something.
- In the subsection &quot;Grassmannian polygon&quot;, second paragraph, I am a bit confused with notations and conventions. If we represent the vector space $v$ by a basis, and put the vectors in columns, we get a matrix of size $md \times m$ and not $m \times md$ right? And then, the action of $GL_{md}$ you are mentioning is simply multiplication on the left?
}} [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 02:30, 15 June 2026 (UTC)</text>
      <sha1>6mf2cq1p5pjnkreuek8fd27vopsygef</sha1>
    </revision>
  </page>
  <page>
    <title>Bully Metric Metonic cycle</title>
    <ns>0</ns>
    <id>329377</id>
    <revision>
      <id>2815663</id>
      <parentid>2812008</parentid>
      <timestamp>2026-06-14T19:22:56Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815663</origin>
      <model>wikitext</model>
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      <text bytes="76812" sha1="sp2djmelm8av40seqa4gyv2m00zu7en" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1996–2109), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2102

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}} || {{nowrap|2098}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}} || {{nowrap|8209 280F B051}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}} || {{nowrap|8209 280F B39C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}} || {{nowrap|8209 280F B6E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}} || {{nowrap|8209 280F BA2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}} || {{nowrap|8209 280F BD70}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}} || {{nowrap|8209 280F C0AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}} || {{nowrap|8209 280F C3ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}} || {{nowrap|8209 280F C729}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}} || {{nowrap|8209 280F CA65}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}} || {{nowrap|8209 280F CDA3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}} || {{nowrap|8209 280F D0E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}} || {{nowrap|8209 280F D427}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}} || {{nowrap|8209 280F D76E}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}

|}</text>
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    <revision>
      <id>2815664</id>
      <parentid>2815663</parentid>
      <timestamp>2026-06-14T19:24:05Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
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      <text bytes="76809" sha1="lnew7ve0zkp1b6zcg4p6nevot4kb0oy" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1996–2109), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2102

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}} || {{nowrap|2098}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}} || {{nowrap|8209 280F B051}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}} || {{nowrap|8209 280F B39C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}} || {{nowrap|8209 280F B6E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}} || {{nowrap|8209 280F BA2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}} || {{nowrap|8209 280F BD70}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}} || {{nowrap|8209 280F C0AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}} || {{nowrap|8209 280F C3ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}} || {{nowrap|8209 280F C729}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}} || {{nowrap|8209 280F CA65}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}} || {{nowrap|8209 280F CDA3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}} || {{nowrap|8209 280F D0E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}} || {{nowrap|8209 280F D427}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}} || {{nowrap|8209 280F D76E}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}

|}</text>
      <sha1>lnew7ve0zkp1b6zcg4p6nevot4kb0oy</sha1>
    </revision>
    <revision>
      <id>2815665</id>
      <parentid>2815664</parentid>
      <timestamp>2026-06-14T19:26:46Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815665</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="76809" sha1="8f6sm4t7b8onptbsbduu2szsqxzagah" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1996–2109), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2102

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}} || {{nowrap|2098}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}} || {{nowrap|8209 280F B051}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}} || {{nowrap|8209 280F B39C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}} || {{nowrap|8209 280F B6E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}} || {{nowrap|8209 280F BA2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}} || {{nowrap|8209 280F BD70}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}} || {{nowrap|8209 280F C0AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}} || {{nowrap|8209 280F C3ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}} || {{nowrap|8209 280F C729}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}} || {{nowrap|8209 280F CA65}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}} || {{nowrap|8209 280F CDA3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}} || {{nowrap|8209 280F D0E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}} || {{nowrap|8209 280F D427}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}} || {{nowrap|8209 280F D76E}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>8f6sm4t7b8onptbsbduu2szsqxzagah</sha1>
    </revision>
    <revision>
      <id>2815666</id>
      <parentid>2815665</parentid>
      <timestamp>2026-06-14T19:27:07Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815666</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="76806" sha1="mdoht9cxs8kbnrpgfk37jcsz0q5jlsl" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1996–2109), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2102

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}} || {{nowrap|2098}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}} || {{nowrap|8209 280F B051}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}} || {{nowrap|8209 280F B39C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}} || {{nowrap|8209 280F B6E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}} || {{nowrap|8209 280F BA2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}} || {{nowrap|8209 280F BD70}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}} || {{nowrap|8209 280F C0AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}} || {{nowrap|8209 280F C3ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}} || {{nowrap|8209 280F C729}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}} || {{nowrap|8209 280F CA65}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}} || {{nowrap|8209 280F CDA3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}} || {{nowrap|8209 280F D0E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}} || {{nowrap|8209 280F D427}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}} || {{nowrap|8209 280F D76E}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>mdoht9cxs8kbnrpgfk37jcsz0q5jlsl</sha1>
    </revision>
    <revision>
      <id>2815668</id>
      <parentid>2815666</parentid>
      <timestamp>2026-06-14T19:28:55Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815668</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="76407" sha1="7upaw2qpe8plhc9ev47t2ix6adt7j3x" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1996–2109), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2102

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>7upaw2qpe8plhc9ev47t2ix6adt7j3x</sha1>
    </revision>
    <revision>
      <id>2815669</id>
      <parentid>2815668</parentid>
      <timestamp>2026-06-14T19:29:50Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815669</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="76410" sha1="3bww9ahbdvnw2r7tbhi1y4oy6pb49uy" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1996–2109), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2102

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>3bww9ahbdvnw2r7tbhi1y4oy6pb49uy</sha1>
    </revision>
    <revision>
      <id>2815680</id>
      <parentid>2815669</parentid>
      <timestamp>2026-06-14T21:35:15Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815680</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="84871" sha1="bq1qyawhq0u83d0dqvdr7ylt5ule21o" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|Date}} || {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}


|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|Date}} || {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>bq1qyawhq0u83d0dqvdr7ylt5ule21o</sha1>
    </revision>
    <revision>
      <id>2815682</id>
      <parentid>2815680</parentid>
      <timestamp>2026-06-14T21:50:15Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815682</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="80642" sha1="srv2ijlhpi3xiw8w1orbu737h7ldszs" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)


|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|Date}} || {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>srv2ijlhpi3xiw8w1orbu737h7ldszs</sha1>
    </revision>
    <revision>
      <id>2815683</id>
      <parentid>2815682</parentid>
      <timestamp>2026-06-14T21:52:05Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815683</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="80640" sha1="q49tm21fvw4xajjmvp13f3lq382cmt5" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>q49tm21fvw4xajjmvp13f3lq382cmt5</sha1>
    </revision>
    <revision>
      <id>2815685</id>
      <parentid>2815683</parentid>
      <timestamp>2026-06-14T21:53:58Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815685</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="84565" sha1="cyxiup4x92g7jlbh7vizfby2zj0oxzs" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>cyxiup4x92g7jlbh7vizfby2zj0oxzs</sha1>
    </revision>
    <revision>
      <id>2815686</id>
      <parentid>2815685</parentid>
      <timestamp>2026-06-14T21:55:14Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815686</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="84569" sha1="3awken5y8qjgssi8492rnpqixjo3tv4" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>3awken5y8qjgssi8492rnpqixjo3tv4</sha1>
    </revision>
    <revision>
      <id>2815687</id>
      <parentid>2815686</parentid>
      <timestamp>2026-06-14T21:56:52Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815687</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="84573" sha1="bpebirypjxfra7y68rqmxivrxru2bej" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>bpebirypjxfra7y68rqmxivrxru2bej</sha1>
    </revision>
    <revision>
      <id>2815690</id>
      <parentid>2815687</parentid>
      <timestamp>2026-06-14T22:01:05Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815690</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="88799" sha1="0xknu993cay4avtpgge44168rrooac6" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>0xknu993cay4avtpgge44168rrooac6</sha1>
    </revision>
    <revision>
      <id>2815691</id>
      <parentid>2815690</parentid>
      <timestamp>2026-06-14T22:04:20Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815691</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="84966" sha1="l9gskke6xiiskxtov3ckkhbcuupcw1p" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1996 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1996 .. 2102)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>l9gskke6xiiskxtov3ckkhbcuupcw1p</sha1>
    </revision>
    <revision>
      <id>2815692</id>
      <parentid>2815691</parentid>
      <timestamp>2026-06-14T22:06:02Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815692</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="84966" sha1="3qbv4976igvxfhcqokn9fui1h9xubnn" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}} || {{nowrap|2099}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}} || {{nowrap|8209 280F DAB7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 20}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}} || {{nowrap|8209 280F DE01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}} || {{nowrap|8209 280F E14C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}} || {{nowrap|8209 280F E493}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}} || {{nowrap|8209 280F E7D8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}} || {{nowrap|8209 280F EB19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}} || {{nowrap|8209 280F EE57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}} || {{nowrap|8209 280F F195}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}} || {{nowrap|8209 280F F4D2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}} || {{nowrap|8209 280F F811}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}} || {{nowrap|8209 280F FB51}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}} || {{nowrap|8209 280F FE93}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}} || {{nowrap|2100}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}} || {{nowrap|8209 2810 01D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}} || {{nowrap|8209 2810 051E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}} || {{nowrap|8209 2810 0867}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}} || {{nowrap|8209 2810 0BB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}} || {{nowrap|8209 2810 0EF8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}} || {{nowrap|8209 2810 123D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}} || {{nowrap|8209 2810 1580}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}} || {{nowrap|8209 2810 18C1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}} || {{nowrap|8209 2810 1C01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}} || {{nowrap|8209 2810 1F40}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}} || {{nowrap|8209 2810 227F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}} || {{nowrap|8209 2810 25BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}} || {{nowrap|8209 2810 2900}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>3qbv4976igvxfhcqokn9fui1h9xubnn</sha1>
    </revision>
    <revision>
      <id>2815693</id>
      <parentid>2815692</parentid>
      <timestamp>2026-06-14T22:08:12Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815693</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="76817" sha1="lebvnyzxfqfkaq9twnexdlqz66yerw7" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}} || {{nowrap|2101}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}} || {{nowrap|8209 2810 2C43}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}} || {{nowrap|8209 2810 2F87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}} || {{nowrap|8209 2810 32CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}} || {{nowrap|8209 2810 3614}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}} || {{nowrap|8209 2810 395A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}} || {{nowrap|8209 2810 3CA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}} || {{nowrap|8209 2810 3FE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}} || {{nowrap|8209 2810 4329}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}} || {{nowrap|8209 2810 466C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}} || {{nowrap|8209 2810 49AD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}} || {{nowrap|8209 2810 4CED}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}} || {{nowrap|8209 2810 502D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>lebvnyzxfqfkaq9twnexdlqz66yerw7</sha1>
    </revision>
    <revision>
      <id>2815694</id>
      <parentid>2815693</parentid>
      <timestamp>2026-06-14T22:11:55Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815694</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="76818" sha1="1v68s85cmhduxgtln96fbxds73p9s70" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>1v68s85cmhduxgtln96fbxds73p9s70</sha1>
    </revision>
    <revision>
      <id>2815695</id>
      <parentid>2815694</parentid>
      <timestamp>2026-06-14T22:18:13Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815695</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="102588" sha1="n4iqkkqp7ch38dpw0h0o8c0z8cywn3t" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}


|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|Date}} || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 27FE 5B81}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 27FE 5EC1}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 27FE 6201}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 27FE 6541}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 15}} || {{nowrap|8209 27FE 6882}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 27FE 6BC3}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 27FE 6F06}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 27FE 724B}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 27FE 7593}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 27FE 78DB}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 27FE 7C22}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 27FE 7F69}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|Date}} || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 6}} || {{nowrap|8209 27FE 85F0}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 27FE 8930}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FE 8C6F}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 5}} || {{nowrap|8209 27FE 8FAD}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 27FE 92EB}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 27FE 962A}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 996B}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 9CAF}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 27FE 9FF6}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 29}} || {{nowrap|8209 27FE A33F}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 28}} || {{nowrap|8209 27FE A689}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|Date}} || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 27FE AD19}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 27FE B05D}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 27FE B39E}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 27FE B6DD}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 24}} || {{nowrap|8209 27FE BA19}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 27FE BD56}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 22}} || {{nowrap|8209 27FE C093}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 27FE C3D3}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 27FE C716}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 27FE CA5B}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 27FE CDA4}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 27FE D0EF}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|Date}} || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 14}} || {{nowrap|8209 27FE D783}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 27FE DAC8}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 27FE DE0A}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 13}} || {{nowrap|8209 27FE E149}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 12}} || {{nowrap|8209 27FE E486}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 11}} || {{nowrap|8209 27FE E7C2}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 10}} || {{nowrap|8209 27FE EAFF}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 27FE EE3D}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 27FE F17E}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 27FE F4C2}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 27FE FB55}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 27FE FEA0}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 27FF 01EA}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 27FF 0531}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FF 0874}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0BB4}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0EF2}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 27FF 122F}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 27FF 156B}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 27FF 18A9}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 27FF 1BE9}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 27FF 1F2C}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 27FF 2272}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 27FF 2905}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 21}} || {{nowrap|8209 27FF 2C4F}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 27FF 2F97}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 21}} || {{nowrap|8209 27FF 32DC}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 27FF 361E}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 27FF 395D}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 17}} || {{nowrap|8209 27FF 3C9B}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 27FF 3FD8}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 15}} || {{nowrap|8209 27FF 4316}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 27FF 4656}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 27FF 4CDD}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 27FF 5023}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 27FF 536B}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 27FF 56B3}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 27FF 59FB}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 27FF 5D41}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 27FF 6085}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 27FF 63C6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 27FF 6706}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 27FF 6A45}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 27FF 6D85}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 27FF 70C5}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>n4iqkkqp7ch38dpw0h0o8c0z8cywn3t</sha1>
    </revision>
    <revision>
      <id>2815696</id>
      <parentid>2815695</parentid>
      <timestamp>2026-06-14T22:24:50Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815696</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="102590" sha1="jb7kem8nubpdrzeruqmgzvh9x05dl76" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 27FE 5B81}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 27FE 5EC1}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 27FE 6201}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 27FE 6541}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 15}} || {{nowrap|8209 27FE 6882}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 27FE 6BC3}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 27FE 6F06}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 27FE 724B}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 27FE 7593}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 27FE 78DB}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 27FE 7C22}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 27FE 7F69}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 6}} || {{nowrap|8209 27FE 85F0}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 27FE 8930}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FE 8C6F}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 5}} || {{nowrap|8209 27FE 8FAD}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 27FE 92EB}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 27FE 962A}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 996B}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 9CAF}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 27FE 9FF6}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 29}} || {{nowrap|8209 27FE A33F}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 28}} || {{nowrap|8209 27FE A689}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|Date}} || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 27FE AD19}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 27FE B05D}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 27FE B39E}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 27FE B6DD}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 24}} || {{nowrap|8209 27FE BA19}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 27FE BD56}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 22}} || {{nowrap|8209 27FE C093}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 27FE C3D3}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 27FE C716}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 27FE CA5B}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 27FE CDA4}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 27FE D0EF}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|Date}} || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 14}} || {{nowrap|8209 27FE D783}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 27FE DAC8}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 27FE DE0A}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 13}} || {{nowrap|8209 27FE E149}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 12}} || {{nowrap|8209 27FE E486}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 11}} || {{nowrap|8209 27FE E7C2}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 10}} || {{nowrap|8209 27FE EAFF}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 27FE EE3D}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 27FE F17E}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 27FE F4C2}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 27FE FB55}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 27FE FEA0}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 27FF 01EA}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 27FF 0531}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FF 0874}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0BB4}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0EF2}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 27FF 122F}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 27FF 156B}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 27FF 18A9}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 27FF 1BE9}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 27FF 1F2C}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 27FF 2272}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 27FF 2905}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 21}} || {{nowrap|8209 27FF 2C4F}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 27FF 2F97}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 21}} || {{nowrap|8209 27FF 32DC}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 27FF 361E}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 27FF 395D}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 17}} || {{nowrap|8209 27FF 3C9B}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 27FF 3FD8}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 15}} || {{nowrap|8209 27FF 4316}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 27FF 4656}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 27FF 4CDD}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 27FF 5023}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 27FF 536B}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 27FF 56B3}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 27FF 59FB}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 27FF 5D41}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 27FF 6085}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 27FF 63C6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 27FF 6706}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 27FF 6A45}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 27FF 6D85}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 27FF 70C5}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}} || {{nowrap|2102}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}} || {{nowrap|8209 2810 536E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}} || {{nowrap|8209 2810 56B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}} || {{nowrap|8209 2810 59F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}} || {{nowrap|8209 2810 5D34}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 16}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}} || {{nowrap|8209 2810 6078}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}} || {{nowrap|8209 2810 63BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 14}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}} || {{nowrap|8209 2810 6703}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}} || {{nowrap|8209 2810 6A4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}} || {{nowrap|8209 2810 6D90}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}} || {{nowrap|8209 2810 70D4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}} || {{nowrap|8209 2810 7418}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>jb7kem8nubpdrzeruqmgzvh9x05dl76</sha1>
    </revision>
    <revision>
      <id>2815698</id>
      <parentid>2815696</parentid>
      <timestamp>2026-06-14T22:30:18Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815698</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="69096" sha1="qnya1kz26a78o7isbp6lrhcevimaxej" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 26}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>qnya1kz26a78o7isbp6lrhcevimaxej</sha1>
    </revision>
    <revision>
      <id>2815701</id>
      <parentid>2815698</parentid>
      <timestamp>2026-06-14T22:37:59Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815701</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="58163" sha1="9ridi1bckrnl538kjsi8nttdjcwalmc" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>9ridi1bckrnl538kjsi8nttdjcwalmc</sha1>
    </revision>
    <revision>
      <id>2815704</id>
      <parentid>2815701</parentid>
      <timestamp>2026-06-14T22:48:30Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815704</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="94324" sha1="llkbwjr7cc3h8o050idg6ykvc2rqeef" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}

|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 27FE 5B81}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 27FE 5EC1}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 27FE 6201}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 27FE 6541}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 15}} || {{nowrap|8209 27FE 6882}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 27FE 6BC3}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 27FE 6F06}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 27FE 724B}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 27FE 7593}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 27FE 78DB}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 27FE 7C22}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 27FE 7F69}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 6}} || {{nowrap|8209 27FE 85F0}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 27FE 8930}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FE 8C6F}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 5}} || {{nowrap|8209 27FE 8FAD}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 27FE 92EB}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 27FE 962A}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 996B}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 9CAF}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 27FE 9FF6}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 29}} || {{nowrap|8209 27FE A33F}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 28}} || {{nowrap|8209 27FE A689}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 27FE AD19}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 27FE B05D}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 27FE B39E}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 27FE B6DD}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 24}} || {{nowrap|8209 27FE BA19}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 27FE BD56}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 22}} || {{nowrap|8209 27FE C093}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 27FE C3D3}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 27FE C716}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 27FE CA5B}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 27FE CDA4}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 27FE D0EF}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 14}} || {{nowrap|8209 27FE D783}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 27FE DAC8}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 27FE DE0A}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 13}} || {{nowrap|8209 27FE E149}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 12}} || {{nowrap|8209 27FE E486}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 11}} || {{nowrap|8209 27FE E7C2}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 10}} || {{nowrap|8209 27FE EAFF}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 27FE EE3D}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 27FE F17E}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 27FE F4C2}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 27FE FB55}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 27FE FEA0}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 27FF 01EA}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 27FF 0531}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FF 0874}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0BB4}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0EF2}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 27FF 122F}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 27FF 156B}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 27FF 18A9}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 27FF 1BE9}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 27FF 1F2C}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 27FF 2272}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 27FF 2905}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 21}} || {{nowrap|8209 27FF 2C4F}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 27FF 2F97}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 21}} || {{nowrap|8209 27FF 32DC}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 27FF 361E}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 27FF 395D}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 17}} || {{nowrap|8209 27FF 3C9B}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 27FF 3FD8}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 15}} || {{nowrap|8209 27FF 4316}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 27FF 4656}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 27FF 4CDD}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 27FF 5023}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 27FF 536B}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 27FF 56B3}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 27FF 59FB}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 27FF 5D41}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 27FF 6085}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 27FF 63C6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 27FF 6706}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 27FF 6A45}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 27FF 6D85}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 27FF 70C5}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1995}} || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 27FF 7748}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 27FF 7A8C}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 27FF 7DD1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 27FF 8117}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FF 845E}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FF 87A4}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 27FF 8AE9}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FF 8E2D}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FF 9170}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 27FF 94B2}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FF 97F3}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>llkbwjr7cc3h8o050idg6ykvc2rqeef</sha1>
    </revision>
    <revision>
      <id>2815708</id>
      <parentid>2815704</parentid>
      <timestamp>2026-06-14T23:38:14Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815708</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="94363" sha1="lt1pp1kmyp3e744au3aeffcf3tx18ce" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|}} || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 27FE 5B81}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 27FE 5EC1}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 27FE 6201}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 27FE 6541}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 15}} || {{nowrap|8209 27FE 6882}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 27FE 6BC3}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 27FE 6F06}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 27FE 724B}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 27FE 7593}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 27FE 78DB}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 27FE 7C22}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 27FE 7F69}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|}} || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 6}} || {{nowrap|8209 27FE 85F0}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 27FE 8930}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FE 8C6F}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 5}} || {{nowrap|8209 27FE 8FAD}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 27FE 92EB}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 27FE 962A}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 996B}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 9CAF}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 27FE 9FF6}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 29}} || {{nowrap|8209 27FE A33F}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 28}} || {{nowrap|8209 27FE A689}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 27FE AD19}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 27FE B05D}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 27FE B39E}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 27FE B6DD}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 24}} || {{nowrap|8209 27FE BA19}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 27FE BD56}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 22}} || {{nowrap|8209 27FE C093}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 27FE C3D3}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 27FE C716}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 27FE CA5B}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 27FE CDA4}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 27FE D0EF}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 14}} || {{nowrap|8209 27FE D783}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 27FE DAC8}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 27FE DE0A}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 13}} || {{nowrap|8209 27FE E149}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 12}} || {{nowrap|8209 27FE E486}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 11}} || {{nowrap|8209 27FE E7C2}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 10}} || {{nowrap|8209 27FE EAFF}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 27FE EE3D}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 27FE F17E}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 27FE F4C2}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 27FE FB55}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 27FE FEA0}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 27FF 01EA}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 27FF 0531}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FF 0874}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0BB4}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0EF2}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 27FF 122F}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 27FF 156B}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 27FF 18A9}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 27FF 1BE9}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 27FF 1F2C}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 27FF 2272}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 27FF 2905}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 21}} || {{nowrap|8209 27FF 2C4F}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 27FF 2F97}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 21}} || {{nowrap|8209 27FF 32DC}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 27FF 361E}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 27FF 395D}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 17}} || {{nowrap|8209 27FF 3C9B}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 27FF 3FD8}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 15}} || {{nowrap|8209 27FF 4316}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 27FF 4656}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 27FF 4CDD}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 27FF 5023}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 27FF 536B}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 27FF 56B3}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 27FF 59FB}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 27FF 5D41}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 27FF 6085}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 27FF 63C6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 27FF 6706}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 27FF 6A45}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 27FF 6D85}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 27FF 70C5}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1995}} || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 27FF 7748}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 27FF 7A8C}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 27FF 7DD1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 27FF 8117}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FF 845E}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FF 87A4}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 27FF 8AE9}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FF 8E2D}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FF 9170}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 27FF 94B2}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FF 97F3}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>lt1pp1kmyp3e744au3aeffcf3tx18ce</sha1>
    </revision>
    <revision>
      <id>2815709</id>
      <parentid>2815708</parentid>
      <timestamp>2026-06-14T23:44:33Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815709</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="90428" sha1="m7g5ujztbsmczkd2tn8q4lqydwtr3lc" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|}} || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 27FE 5B81}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 27FE 5EC1}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 27FE 6201}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 27FE 6541}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 15}} || {{nowrap|8209 27FE 6882}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 27FE 6BC3}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 27FE 6F06}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 27FE 724B}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 27FE 7593}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 27FE 78DB}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 27FE 7C22}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 27FE 7F69}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}

|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 27FE 82AD}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 27FE 85F0}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 27FE 8930}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 27FE 8C6F}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 27FE 8FAD}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 27FE 92EB}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 27FE 962A}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 996B}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 27FE 9CAF}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 27FE 9FF6}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 27FE A33F}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 27FE A689}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 27FE AD19}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 27FE B05D}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 27FE B39E}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 27FE B6DD}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 27FE BA19}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 27FE BD56}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 27FE C093}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 27FE C3D3}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 27FE C716}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 27FE CA5B}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 27FE CDA4}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 27FE D0EF}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 27FE D43A}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 27FE D783}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 27FE DAC8}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 27FE DE0A}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 27FE E149}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 27FE E486}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 27FE E7C2}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 27FE EAFF}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 27FE EE3D}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 27FE F17E}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 27FE F4C2}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 27FE FB55}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 27FE FEA0}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 27FF 01EA}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 27FF 0531}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FF 0874}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0BB4}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 27FF 0EF2}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 27FF 122F}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 27FF 156B}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 27FF 18A9}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 27FF 1BE9}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 27FF 1F2C}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 27FF 2272}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 22}} || {{nowrap|8209 27FF 2905}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 27FF 2C4F}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 27FF 2F97}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 27FF 32DC}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 27FF 361E}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 27FF 395D}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 27FF 3C9B}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 27FF 3FD8}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 27FF 4316}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 27FF 4656}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 27FF 4CDD}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 27FF 5023}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 27FF 536B}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 27FF 56B3}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 27FF 59FB}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 27FF 5D41}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 27FF 6085}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 27FF 63C6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 27FF 6706}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 27FF 6A45}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 27FF 6D85}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 27FF 70C5}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1995}} || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 27FF 7748}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 27FF 7A8C}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 27FF 7DD1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 27FF 8117}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 27FF 845E}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 27FF 87A4}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 27FF 8AE9}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 27FF 8E2D}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 27FF 9170}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 27FF 94B2}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 27FF 97F3}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 20}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>m7g5ujztbsmczkd2tn8q4lqydwtr3lc</sha1>
    </revision>
    <revision>
      <id>2815712</id>
      <parentid>2815709</parentid>
      <timestamp>2026-06-14T23:54:31Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815712</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="90428" sha1="nbqd103sniteyuztf0s6wowrjnxk4gi" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|}} || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 27FE 5B81}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 27FE 5EC1}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 27FE 6201}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 27FE 6541}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 15}} || {{nowrap|8209 27FE 6882}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 27FE 6BC3}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 27FE 6F06}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 27FE 724B}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 27FE 7593}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 27FE 78DB}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 27FE 7C22}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 27FE 7F69}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}

|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 27FE 82AD}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 27FE 85F0}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 27FE 8930}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 27FE 8C6F}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 27FE 8FAD}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 27FE 92EB}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 27FE 962A}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 996B}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 27FE 9CAF}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 27FE 9FF6}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 27FE A33F}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 27FE A689}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 27FE AD19}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 27FE B05D}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 27FE B39E}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 27FE B6DD}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 27FE BA19}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 27FE BD56}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 27FE C093}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 27FE C3D3}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 27FE C716}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 27FE CA5B}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 27FE CDA4}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 27FE D0EF}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 27FE D43A}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 27FE D783}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 27FE DAC8}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 27FE DE0A}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 27FE E149}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 27FE E486}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 27FE E7C2}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 27FE EAFF}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 27FE EE3D}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 27FE F17E}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 27FE F4C2}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 27FE FB55}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 27FE FEA0}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 27FF 01EA}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 27FF 0531}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FF 0874}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0BB4}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 27FF 0EF2}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 27FF 122F}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 27FF 156B}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 27FF 18A9}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 27FF 1BE9}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 27FF 1F2C}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 27FF 2272}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 22}} || {{nowrap|8209 27FF 2905}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 27FF 2C4F}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 27FF 2F97}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 27FF 32DC}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 27FF 361E}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 27FF 395D}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 27FF 3C9B}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 27FF 3FD8}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 27FF 4316}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 27FF 4656}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 27FF 4CDD}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 27FF 5023}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 27FF 536B}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 27FF 56B3}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 27FF 59FB}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 27FF 5D41}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 27FF 6085}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 27FF 63C6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 27FF 6706}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 27FF 6A45}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 27FF 6D85}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 27FF 70C5}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1995}} || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 27FF 7748}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 27FF 7A8C}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 27FF 7DD1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 27FF 8117}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 27FF 845E}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 27FF 87A4}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 27FF 8AE9}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 27FF 8E2D}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 27FF 9170}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 27FF 94B2}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 27FF 97F3}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 23}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 19}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>nbqd103sniteyuztf0s6wowrjnxk4gi</sha1>
    </revision>
    <revision>
      <id>2815713</id>
      <parentid>2815712</parentid>
      <timestamp>2026-06-15T00:04:15Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815713</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="80848" sha1="5dqghsqff440r76azrou49g2qyydmbs" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|}} || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 27FE 5B81}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 27FE 5EC1}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 27FE 6201}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 27FE 6541}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 15}} || {{nowrap|8209 27FE 6882}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 27FE 6BC3}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 27FE 6F06}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 27FE 724B}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 27FE 7593}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 27FE 78DB}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 27FE 7C22}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 27FE 7F69}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}

|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 27FE 82AD}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 27FE 85F0}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 27FE 8930}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 27FE 8C6F}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 27FE 8FAD}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 27FE 92EB}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 27FE 962A}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 996B}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 27FE 9CAF}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 27FE 9FF6}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 27FE A33F}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 27FE A689}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 27FE AD19}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 27FE B05D}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 27FE B39E}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 27FE B6DD}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 27FE BA19}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 27FE BD56}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 27FE C093}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 27FE C3D3}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 27FE C716}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 27FE CA5B}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 27FE CDA4}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 27FE D0EF}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 27FE D43A}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 27FE D783}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 27FE DAC8}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 27FE DE0A}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 27FE E149}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 27FE E486}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 27FE E7C2}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 27FE EAFF}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 27FE EE3D}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 27FE F17E}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 27FE F4C2}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 27FE FB55}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 27FE FEA0}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 27FF 01EA}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 27FF 0531}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FF 0874}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0BB4}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 27FF 0EF2}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 27FF 122F}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 27FF 156B}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 27FF 18A9}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 27FF 1BE9}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 27FF 1F2C}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 27FF 2272}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 22}} || {{nowrap|8209 27FF 2905}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 27FF 2C4F}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 27FF 2F97}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 27FF 32DC}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 27FF 361E}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 27FF 395D}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 27FF 3C9B}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 27FF 3FD8}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 27FF 4316}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 27FF 4656}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 27FF 4CDD}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 27FF 5023}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 27FF 536B}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 27FF 56B3}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 27FF 59FB}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 27FF 5D41}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 27FF 6085}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 27FF 63C6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 27FF 6706}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 27FF 6A45}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 27FF 6D85}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 27FF 70C5}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1995}} || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 27FF 7748}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 27FF 7A8C}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 27FF 7DD1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 27FF 8117}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 27FF 845E}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 27FF 87A4}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 27FF 8AE9}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 27FF 8E2D}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 27FF 9170}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 27FF 94B2}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 27FF 97F3}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}


|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 19}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>5dqghsqff440r76azrou49g2qyydmbs</sha1>
    </revision>
    <revision>
      <id>2815714</id>
      <parentid>2815713</parentid>
      <timestamp>2026-06-15T00:11:03Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815714</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="79488" sha1="qigz3ttklff2zu2ld1wcqjddvvpglx3" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|}} || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 27FE 5B81}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 27FE 5EC1}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 27FE 6201}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 27FE 6541}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 15}} || {{nowrap|8209 27FE 6882}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 27FE 6BC3}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 27FE 6F06}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 27FE 724B}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 27FE 7593}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 27FE 78DB}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 27FE 7C22}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 27FE 7F69}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}

|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 27FE 82AD}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 27FE 85F0}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 27FE 8930}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 27FE 8C6F}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 27FE 8FAD}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 27FE 92EB}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 27FE 962A}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 996B}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 27FE 9CAF}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 27FE 9FF6}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 27FE A33F}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 27FE A689}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 27FE AD19}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 27FE B05D}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 27FE B39E}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 27FE B6DD}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 27FE BA19}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 27FE BD56}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 27FE C093}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 27FE C3D3}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 27FE C716}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 27FE CA5B}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 27FE CDA4}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 27FE D0EF}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 27FE D43A}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 27FE D783}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 27FE DAC8}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 27FE DE0A}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 27FE E149}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 27FE E486}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 27FE E7C2}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 27FE EAFF}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 27FE EE3D}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 27FE F17E}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 27FE F4C2}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 27FE FB55}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 27FE FEA0}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 27FF 01EA}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 27FF 0531}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FF 0874}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0BB4}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 27FF 0EF2}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 27FF 122F}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 27FF 156B}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 27FF 18A9}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 27FF 1BE9}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 27FF 1F2C}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 27FF 2272}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 22}} || {{nowrap|8209 27FF 2905}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 27FF 2C4F}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 27FF 2F97}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 27FF 32DC}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 27FF 361E}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 27FF 395D}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 27FF 3C9B}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 27FF 3FD8}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 27FF 4316}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 27FF 4656}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 27FF 4CDD}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 27FF 5023}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 27FF 536B}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 27FF 56B3}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 27FF 59FB}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 27FF 5D41}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 27FF 6085}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 27FF 63C6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 27FF 6706}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 27FF 6A45}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 27FF 6D85}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 27FF 70C5}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1995}} || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 27FF 7748}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 27FF 7A8C}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 27FF 7DD1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 27FF 8117}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 27FF 845E}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 27FF 87A4}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 27FF 8AE9}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 27FF 8E2D}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 27FF 9170}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 27FF 94B2}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 27FF 97F3}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 19}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>qigz3ttklff2zu2ld1wcqjddvvpglx3</sha1>
    </revision>
    <revision>
      <id>2815715</id>
      <parentid>2815714</parentid>
      <timestamp>2026-06-15T00:12:46Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815715</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="79474" sha1="d3z0hk841xpbvpwxp40fibh4y4mxd9r" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|}} || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 27FE 5B81}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 27FE 5EC1}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 27FE 6201}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 27FE 6541}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 15}} || {{nowrap|8209 27FE 6882}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 27FE 6BC3}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 27FE 6F06}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 27FE 724B}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 27FE 7593}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 27FE 78DB}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 27FE 7C22}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 27FE 7F69}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}

|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 27FE 82AD}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 27FE 85F0}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 27FE 8930}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 27FE 8C6F}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 27FE 8FAD}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 27FE 92EB}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 27FE 962A}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 996B}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 27FE 9CAF}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 27FE 9FF6}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 27FE A33F}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 27FE A689}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 27FE AD19}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 27FE B05D}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 27FE B39E}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 27FE B6DD}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 27FE BA19}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 27FE BD56}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 27FE C093}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 27FE C3D3}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 27FE C716}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 27FE CA5B}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 27FE CDA4}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 27FE D0EF}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 27FE D43A}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 27FE D783}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 27FE DAC8}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 27FE DE0A}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 27FE E149}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 27FE E486}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 27FE E7C2}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 27FE EAFF}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 27FE EE3D}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 27FE F17E}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 27FE F4C2}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 27FE FB55}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 27FE FEA0}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 27FF 01EA}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 27FF 0531}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FF 0874}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0BB4}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 27FF 0EF2}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 27FF 122F}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 27FF 156B}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 27FF 18A9}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 27FF 1BE9}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 27FF 1F2C}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 27FF 2272}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 22}} || {{nowrap|8209 27FF 2905}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 27FF 2C4F}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 27FF 2F97}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 27FF 32DC}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 27FF 361E}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 27FF 395D}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 27FF 3C9B}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 27FF 3FD8}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 27FF 4316}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 27FF 4656}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 27FF 4CDD}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 27FF 5023}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 27FF 536B}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 27FF 56B3}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 27FF 59FB}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 27FF 5D41}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 27FF 6085}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 27FF 63C6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 27FF 6706}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 27FF 6A45}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 27FF 6D85}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 27FF 70C5}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;font-weight: bold; background-color: #eaecf0;&quot;
|| {{nowrap|}} || {{nowrap|1995}} || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 27FF 7748}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 27FF 7A8C}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 27FF 7DD1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 27FF 8117}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 27FF 845E}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 27FF 87A4}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 27FF 8AE9}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 27FF 8E2D}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 27FF 9170}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 27FF 94B2}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 27FF 97F3}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 19}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>d3z0hk841xpbvpwxp40fibh4y4mxd9r</sha1>
    </revision>
    <revision>
      <id>2815716</id>
      <parentid>2815715</parentid>
      <timestamp>2026-06-15T00:19:02Z</timestamp>
      <contributor>
        <username>Unitfreak</username>
        <id>695864</id>
      </contributor>
      <comment>/* The New Moon Solstice */</comment>
      <origin>2815716</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="79522" sha1="h9rnxaiz37ih16c479mqgn5xp47bydd" xml:space="preserve">[[Bully_Metric|Bully Metric Main Page]]&lt;br /&gt;
[[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]&lt;br /&gt;
[[Bully_Metric_Metonic_cycle|The Metonic Cycle in Bully Metric]]&lt;br /&gt;
[https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]&lt;br /&gt;

The '''Metonic cycle''' is a period of approximately 19 solar years, after which the Moon's phases recur on the same calendar dates. This cycle arises because 19 solar years and 235 synodic months nearly coincide.

[[File:Bully_Metric_Metonic_Cycle.png|thumb|center|650 px| Figure 1: The Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years.]]

As shown in Figure 1, the Moon’s phase &quot;advances&quot; by approximately {{frac|7|19}} of a lunar cycle when observed on the same day in subsequent years. For example, if a '''New Moon''' occurs on the December Solstice of 2014:
* The 2015 solstice will feature a '''Waxing Gibbous Moon''' (an advancement of ~{{frac|7|19}}).
* The 2016 solstice will feature a '''Third Quarter Moon''' (an advancement of ~{{frac|14|19}}).
* The 2017 solstice will feature a '''Waxing Crescent Moon''' (an advancement of ~{{frac|21|19}}).
* And the 2033 solstice will feature a '''New Moon''' (an advancement of 7 complete cycles).

Within this 19-year span, significant &quot;near-matches&quot; occur at the 8-year and 11-year marks. At 8 years, the drift reaches {{frac|56|19}} (approx. 2.95 cycles); at 11 years, it reaches {{frac|77|19}} (approx. 4.05 cycles). These intervals represent points where the lunar-solar alignment falls just short or just past a full-integer &quot;reset,&quot; which eventually concludes at the 19-year mark.

=== The New Moon Solstice ===
The darkest nights in the Northern Hemisphere occur when the '''December Solstice''' coincides with a '''New Moon'''. The darkest nights in the Southern Hemisphere occur when the '''June Solstice''' coincides with a '''New Moon'''. The Metonic cycle predicts this alignment every 19 years, with significant &quot;near-matches&quot; at the 8th- and 11th-year marks.

Table 1 illustrates Metonic cycles over a one-century period (1984–2097), listing the approximate date and Bully timestamp for every New Moon during the century. Red cells indicate the New Moon Solstice alignment every 19 years. Yellow cells indicate the New Moon Solstice near-alignments on the 8th- and 11th-year marks of the Metonic cycle.

{| class=&quot;wikitable&quot; style=&quot;text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;&quot;
|+ Table 1: New Moon Bully Timestamps 1984 .. 2097

|- style=&quot;background-color: #eaecf0; font-size: medium; font-weight: bold;&quot;
! rowspan=&quot;2&quot; style=&quot;padding: 10px; font-size: large;&quot; | Metonic Cycle
! colspan=&quot;7&quot; style=&quot;padding: 10px;&quot; | Every New Moon (1984 .. 2097)

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|1984}} || {{nowrap|2003}} || {{nowrap|2022}} || {{nowrap|2041}} || {{nowrap|2060}} || {{nowrap|2079}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 2}} || {{nowrap|8209 27FD B855}} || {{nowrap|8209 2800 B6FC}} || {{nowrap|8209 2803 B5AC}} || {{nowrap|8209 2806 B45E}} || {{nowrap|8209 2809 B30D}} || {{nowrap|8209 280C B1B3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 1}} || {{nowrap|8209 27FD BB9F}} || {{nowrap|8209 2800 BA41}} || {{nowrap|8209 2803 B8ED}} || {{nowrap|8209 2806 B79F}} || {{nowrap|8209 2809 B650}} || {{nowrap|8209 280C B4FB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 2}} || {{nowrap|8209 27FD BEE9}} || {{nowrap|8209 2800 BD88}} || {{nowrap|8209 2803 BC2F}} || {{nowrap|8209 2806 BADE}} || {{nowrap|8209 2809 B991}} || {{nowrap|8209 280C B840}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 1}} || {{nowrap|8209 27FD C232}} || {{nowrap|8209 2800 C0D0}} || {{nowrap|8209 2803 BF72}} || {{nowrap|8209 2806 BE1E}} || {{nowrap|8209 2809 BCD0}} || {{nowrap|8209 280C BB81}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FD C579}} || {{nowrap|8209 2800 C418}} || {{nowrap|8209 2803 C2B7}} || {{nowrap|8209 2806 C15E}} || {{nowrap|8209 2809 C00E}} || {{nowrap|8209 280C BEC1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 29}} || {{nowrap|8209 27FD C8BC}} || {{nowrap|8209 2800 C75F}} || {{nowrap|8209 2803 C5FD}} || {{nowrap|8209 2806 C4A0}} || {{nowrap|8209 2809 C34C}} || {{nowrap|8209 280C C1FE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 28}} || {{nowrap|8209 27FD CBFD}} || {{nowrap|8209 2800 CAA4}} || {{nowrap|8209 2803 C943}} || {{nowrap|8209 2806 C7E2}} || {{nowrap|8209 2809 C68A}} || {{nowrap|8209 280C C53A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 27}} || {{nowrap|8209 27FD CF3B}} || {{nowrap|8209 2800 CDE7}} || {{nowrap|8209 2803 CC89}} || {{nowrap|8209 2806 CB27}} || {{nowrap|8209 2809 C9CA}} || {{nowrap|8209 280C C877}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 26}} || {{nowrap|8209 27FD D278}} || {{nowrap|8209 2800 D127}} || {{nowrap|8209 2803 CFCE}} || {{nowrap|8209 2806 CE6D}} || {{nowrap|8209 2809 CD0D}} || {{nowrap|8209 280C CBB5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 24}} || {{nowrap|8209 27FD D5B5}} || {{nowrap|8209 2800 D467}} || {{nowrap|8209 2803 D312}} || {{nowrap|8209 2806 D1B4}} || {{nowrap|8209 2809 D052}} || {{nowrap|8209 280C CEF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 24}} || {{nowrap|8209 27FD D8F4}} || {{nowrap|8209 2800 D7A6}} || {{nowrap|8209 2803 D656}} || {{nowrap|8209 2806 D4FC}} || {{nowrap|8209 2809 D39B}} || {{nowrap|8209 280C D23B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 22}} || {{nowrap|8209 27FD DC35}} || {{nowrap|8209 2800 DAE7}} || {{nowrap|8209 2803 D998}} || {{nowrap|8209 2806 D844}} || {{nowrap|8209 2809 D6E6}} || {{nowrap|8209 280C D583}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 22}} || {{nowrap|8209 27FD DF78}} || {{nowrap|8209 2800 DE27}} || {{nowrap|8209 2803 DCDA}} || {{nowrap|8209 2806 DB89}} || {{nowrap|8209 2809 DA2F}} || {{nowrap|8209 280C D8CE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1985}} || {{nowrap|2004}} || {{nowrap|2023}} || {{nowrap|2042}} || {{nowrap|2061}} || {{nowrap|2080}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 21}} || {{nowrap|8209 27FD E2BE}} || {{nowrap|8209 2800 E169}} || {{nowrap|8209 2803 E01A}} || {{nowrap|8209 2806 DECC}} || {{nowrap|8209 2809 DD77}} || {{nowrap|8209 280C DC19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 19}} || {{nowrap|8209 27FD E605}} || {{nowrap|8209 2800 E4AC}} || {{nowrap|8209 2803 E35B}} || {{nowrap|8209 2806 E20D}} || {{nowrap|8209 2809 E0BC}} || {{nowrap|8209 280C DF63}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 20}} || {{nowrap|8209 27FD E94E}} || {{nowrap|8209 2800 E7EF}} || {{nowrap|8209 2803 E69B}} || {{nowrap|8209 2806 E54D}} || {{nowrap|8209 2809 E3FE}} || {{nowrap|8209 280C E2AA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 19}} || {{nowrap|8209 27FD EC96}} || {{nowrap|8209 2800 EB35}} || {{nowrap|8209 2803 E9DC}} || {{nowrap|8209 2806 E88B}} || {{nowrap|8209 2809 E73E}} || {{nowrap|8209 280C E5ED}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 19}} || {{nowrap|8209 27FD EFDE}} || {{nowrap|8209 2800 EE7B}} || {{nowrap|8209 2803 ED1E}} || {{nowrap|8209 2806 EBCA}} || {{nowrap|8209 2809 EA7B}} || {{nowrap|8209 280C E92D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 17}} || {{nowrap|8209 27FD F323}} || {{nowrap|8209 2800 F1C2}} || {{nowrap|8209 2803 F061}} || {{nowrap|8209 2806 EF08}} || {{nowrap|8209 2809 EDB8}} || {{nowrap|8209 280C EC6A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 17}} || {{nowrap|8209 27FD F665}} || {{nowrap|8209 2800 F508}} || {{nowrap|8209 2803 F3A5}} || {{nowrap|8209 2806 F248}} || {{nowrap|8209 2809 F0F4}} || {{nowrap|8209 280C EFA6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 15}} || {{nowrap|8209 27FD F9A5}} || {{nowrap|8209 2800 F84C}} || {{nowrap|8209 2803 F6EB}} || {{nowrap|8209 2806 F58B}} || {{nowrap|8209 2809 F432}} || {{nowrap|8209 280C F2E2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 13}} || {{nowrap|8209 27FD FCE4}} || {{nowrap|8209 2800 FB90}} || {{nowrap|8209 2803 FA32}} || {{nowrap|8209 2806 F8D0}} || {{nowrap|8209 2809 F774}} || {{nowrap|8209 280C F620}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 13}} || {{nowrap|8209 27FE 0023}} || {{nowrap|8209 2800 FED3}} || {{nowrap|8209 2803 FD7A}} || {{nowrap|8209 2806 FC19}} || {{nowrap|8209 2809 FAB8}} || {{nowrap|8209 280C F961}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 11}} || {{nowrap|8209 27FE 0363}} || {{nowrap|8209 2801 0214}} || {{nowrap|8209 2804 00C0}} || {{nowrap|8209 2806 FF63}} || {{nowrap|8209 2809 FE00}} || {{nowrap|8209 280C FCA4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 11}} || {{nowrap|8209 27FE 06A3}} || {{nowrap|8209 2801 0556}} || {{nowrap|8209 2804 0405}} || {{nowrap|8209 2807 02AC}} || {{nowrap|8209 280A 014B}} || {{nowrap|8209 280C FFEA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1986}} || {{nowrap|2005}} || {{nowrap|2024}} || {{nowrap|2043}} || {{nowrap|2062}} || {{nowrap|2081}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 10}} || {{nowrap|8209 27FE 09E5}} || {{nowrap|8209 2801 0896}} || {{nowrap|8209 2804 0748}} || {{nowrap|8209 2807 05F3}} || {{nowrap|8209 280A 0496}} || {{nowrap|8209 280D 0334}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 8}} || {{nowrap|8209 27FE 0D28}} || {{nowrap|8209 2801 0BD7}} || {{nowrap|8209 2804 0A89}} || {{nowrap|8209 2807 0938}} || {{nowrap|8209 280A 07E0}} || {{nowrap|8209 280D 067E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 10}} || {{nowrap|8209 27FE 106D}} || {{nowrap|8209 2801 0F17}} || {{nowrap|8209 2804 0DC9}} || {{nowrap|8209 2807 0C7B}} || {{nowrap|8209 280A 0B27}} || {{nowrap|8209 280D 09C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 8}} || {{nowrap|8209 27FE 13B3}} || {{nowrap|8209 2801 1259}} || {{nowrap|8209 2804 1108}} || {{nowrap|8209 2807 0FBB}} || {{nowrap|8209 280A 0E6A}} || {{nowrap|8209 280D 0D11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 8}} || {{nowrap|8209 27FE 16FA}} || {{nowrap|8209 2801 159C}} || {{nowrap|8209 2804 1447}} || {{nowrap|8209 2807 12F9}} || {{nowrap|8209 280A 11AA}} || {{nowrap|8209 280D 1056}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 6}} || {{nowrap|8209 27FE 1A41}} || {{nowrap|8209 2801 18DF}} || {{nowrap|8209 2804 1786}} || {{nowrap|8209 2807 1635}} || {{nowrap|8209 280A 14E8}} || {{nowrap|8209 280D 1397}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 5}} || {{nowrap|8209 27FE 1D86}} || {{nowrap|8209 2801 1C24}} || {{nowrap|8209 2804 1AC6}} || {{nowrap|8209 2807 1972}} || {{nowrap|8209 280A 1824}} || {{nowrap|8209 280D 16D5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 4}} || {{nowrap|8209 27FE 20CB}} || {{nowrap|8209 2801 1F6A}} || {{nowrap|8209 2804 1E09}} || {{nowrap|8209 2807 1CB0}} || {{nowrap|8209 280A 1B60}} || {{nowrap|8209 280D 1A12}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 3}} || {{nowrap|8209 27FE 240E}} || {{nowrap|8209 2801 22B1}} || {{nowrap|8209 2804 214E}} || {{nowrap|8209 2807 1FF1}} || {{nowrap|8209 280A 1E9D}} || {{nowrap|8209 280D 1D4F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 2}} || {{nowrap|8209 27FE 2750}} || {{nowrap|8209 2801 25F7}} || {{nowrap|8209 2804 2496}} || {{nowrap|8209 2807 2336}} || {{nowrap|8209 280A 21DE}} || {{nowrap|8209 280D 208D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 1}} || {{nowrap|8209 27FE 2A91}} || {{nowrap|8209 2801 293D}} || {{nowrap|8209 2804 27E0}} || {{nowrap|8209 2807 267E}} || {{nowrap|8209 280A 2521}} || {{nowrap|8209 280D 23CD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 1}} || {{nowrap|8209 27FE 2DD2}} || {{nowrap|8209 2801 2C81}} || {{nowrap|8209 2804 2B29}} || {{nowrap|8209 2807 29C8}} || {{nowrap|8209 280A 2867}} || {{nowrap|8209 280D 270F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 30}} || {{nowrap|8209 27FE 3112}} || {{nowrap|8209 2801 2FC4}} || {{nowrap|8209 2804 2E70}} || {{nowrap|8209 2807 2D13}} || {{nowrap|8209 280A 2BB0}} || {{nowrap|8209 280D 2A53}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1987}} || {{nowrap|2006}} || {{nowrap|2025}} || {{nowrap|2044}} || {{nowrap|2063}} || {{nowrap|2082}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 28}} || {{nowrap|8209 27FE 3453}} || {{nowrap|8209 2801 3305}} || {{nowrap|8209 2804 31B5}} || {{nowrap|8209 2807 305C}} || {{nowrap|8209 280A 2EFB}} || {{nowrap|8209 280D 2D9B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 27}} || {{nowrap|8209 27FE 3794}} || {{nowrap|8209 2801 3645}} || {{nowrap|8209 2804 34F7}} || {{nowrap|8209 2807 33A3}} || {{nowrap|8209 280A 3246}} || {{nowrap|8209 280D 30E4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 29}} || {{nowrap|8209 27FE 3AD6}} || {{nowrap|8209 2801 3985}} || {{nowrap|8209 2804 3837}} || {{nowrap|8209 2807 36E7}} || {{nowrap|8209 280A 358F}} || {{nowrap|8209 280D 342E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 27}} || {{nowrap|8209 27FE 3E19}} || {{nowrap|8209 2801 3CC4}} || {{nowrap|8209 2804 3B76}} || {{nowrap|8209 2807 3A27}} || {{nowrap|8209 280A 38D3}} || {{nowrap|8209 280D 3776}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 27}} || {{nowrap|8209 27FE 415E}} || {{nowrap|8209 2801 4004}} || {{nowrap|8209 2804 3EB3}} || {{nowrap|8209 2807 3D65}} || {{nowrap|8209 280A 3C14}} || {{nowrap|8209 280D 3ABC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 25}} || {{nowrap|8209 27FE 44A3}} || {{nowrap|8209 2801 4345}} || {{nowrap|8209 2804 41F0}} || {{nowrap|8209 2807 40A1}} || {{nowrap|8209 280A 3F53}} || {{nowrap|8209 280D 3DFE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 24}} || {{nowrap|8209 27FE 47E9}} || {{nowrap|8209 2801 4687}} || {{nowrap|8209 2804 452E}} || {{nowrap|8209 2807 43DD}} || {{nowrap|8209 280A 4290}} || {{nowrap|8209 280D 413F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 23}} || {{nowrap|8209 27FE 4B2F}} || {{nowrap|8209 2801 49CD}} || {{nowrap|8209 2804 486F}} || {{nowrap|8209 2807 471B}} || {{nowrap|8209 280A 45CD}} || {{nowrap|8209 280D 447E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 21}} || {{nowrap|8209 27FE 4E75}} || {{nowrap|8209 2801 4D14}} || {{nowrap|8209 2804 4BB3}} || {{nowrap|8209 2807 4A5B}} || {{nowrap|8209 280A 490A}} || {{nowrap|8209 280D 47BD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 20}} || {{nowrap|8209 27FE 51BA}} || {{nowrap|8209 2801 505D}} || {{nowrap|8209 2804 4EFB}} || {{nowrap|8209 2807 4D9E}} || {{nowrap|8209 280A 4C4A}} || {{nowrap|8209 280D 4AFB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 19}} || {{nowrap|8209 27FE 54FE}} || {{nowrap|8209 2801 53A5}} || {{nowrap|8209 2804 5245}} || {{nowrap|8209 2807 50E4}} || {{nowrap|8209 280A 4F8B}} || {{nowrap|8209 280D 4E3B}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 19}} || {{nowrap|8209 27FE 5840}} || {{nowrap|8209 2801 56EC}} || {{nowrap|8209 2804 558F}} || {{nowrap|8209 2807 542D}} || {{nowrap|8209 280A 52D0}} || {{nowrap|8209 280D 517C}}

|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| {{nowrap|}} || {{nowrap|1988}} || {{nowrap|2007}} || {{nowrap|2026}} || {{nowrap|2045}} || {{nowrap|2064}} || {{nowrap|2083}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 18}} || {{nowrap|8209 27FE 5B81}} || {{nowrap|8209 2801 5A31}} || {{nowrap|8209 2804 58D9}} || {{nowrap|8209 2807 5778}} || {{nowrap|8209 280A 5617}} || {{nowrap|8209 280D 54BF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 16}} || {{nowrap|8209 27FE 5EC1}} || {{nowrap|8209 2801 5D73}} || {{nowrap|8209 2804 5C20}} || {{nowrap|8209 2807 5AC3}} || {{nowrap|8209 280A 5961}} || {{nowrap|8209 280D 5804}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 18}} || {{nowrap|8209 27FE 6201}} || {{nowrap|8209 2801 60B4}} || {{nowrap|8209 2804 5F64}} || {{nowrap|8209 2807 5E0C}} || {{nowrap|8209 280A 5CAB}} || {{nowrap|8209 280D 5B4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 16}} || {{nowrap|8209 27FE 6541}} || {{nowrap|8209 2801 63F3}} || {{nowrap|8209 2804 62A5}} || {{nowrap|8209 2807 6151}} || {{nowrap|8209 280A 5FF4}} || {{nowrap|8209 280D 5E92}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 15}} || {{nowrap|8209 27FE 6882}} || {{nowrap|8209 2801 6730}} || {{nowrap|8209 2804 65E2}} || {{nowrap|8209 2807 6492}} || {{nowrap|8209 280A 633A}} || {{nowrap|8209 280D 61D9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 14}} || {{nowrap|8209 27FE 6BC3}} || {{nowrap|8209 2801 6A6D}} || {{nowrap|8209 2804 691F}} || {{nowrap|8209 2807 67D0}} || {{nowrap|8209 280A 667C}} || {{nowrap|8209 280D 651F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 13}} || {{nowrap|8209 27FE 6F06}} || {{nowrap|8209 2801 6DAC}} || {{nowrap|8209 2804 6C5B}} || {{nowrap|8209 2807 6B0D}} || {{nowrap|8209 280A 69BD}} || {{nowrap|8209 280D 6864}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 12}} || {{nowrap|8209 27FE 724B}} || {{nowrap|8209 2801 70ED}} || {{nowrap|8209 2804 6F98}} || {{nowrap|8209 2807 6E4A}} || {{nowrap|8209 280A 6CFC}} || {{nowrap|8209 280D 6BA7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 11}} || {{nowrap|8209 27FE 7593}} || {{nowrap|8209 2801 7431}} || {{nowrap|8209 2804 72D8}} || {{nowrap|8209 2807 7187}} || {{nowrap|8209 280A 703A}} || {{nowrap|8209 280D 6EE9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 10}} || {{nowrap|8209 27FE 78DB}} || {{nowrap|8209 2801 7779}} || {{nowrap|8209 2804 761B}} || {{nowrap|8209 2807 74C6}} || {{nowrap|8209 280A 7378}} || {{nowrap|8209 280D 7229}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 8}} || {{nowrap|8209 27FE 7C22}} || {{nowrap|8209 2801 7AC2}} || {{nowrap|8209 2804 7961}} || {{nowrap|8209 2807 7808}} || {{nowrap|8209 280A 76B7}} || {{nowrap|8209 280D 7569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 8}} || {{nowrap|8209 27FE 7F69}} || {{nowrap|8209 2801 7E0C}} || {{nowrap|8209 2804 7CAA}} || {{nowrap|8209 2807 7B4C}} || {{nowrap|8209 280A 79F8}} || {{nowrap|8209 280D 78A9}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1989}} || {{nowrap|2008}} || {{nowrap|2027}} || {{nowrap|2046}} || {{nowrap|2065}} || {{nowrap|2084}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 6}} || {{nowrap|8209 27FE 82AD}} || {{nowrap|8209 2801 8155}} || {{nowrap|8209 2804 7FF5}} || {{nowrap|8209 2807 7E94}} || {{nowrap|8209 280A 7D3B}} || {{nowrap|8209 280D 7BEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 5}} || {{nowrap|8209 27FE 85F0}} || {{nowrap|8209 2801 849D}} || {{nowrap|8209 2804 8340}} || {{nowrap|8209 2807 81DE}} || {{nowrap|8209 280A 8080}} || {{nowrap|8209 280D 7F2C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 6}} || {{nowrap|8209 27FE 8930}} || {{nowrap|8209 2801 87E1}} || {{nowrap|8209 2804 8689}} || {{nowrap|8209 2807 8529}} || {{nowrap|8209 280A 83C8}} || {{nowrap|8209 280D 826F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 5}} || {{nowrap|8209 27FE 8C6F}} || {{nowrap|8209 2801 8B21}} || {{nowrap|8209 2804 89CE}} || {{nowrap|8209 2807 8872}} || {{nowrap|8209 280A 8710}} || {{nowrap|8209 280D 85B2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 4}} || {{nowrap|8209 27FE 8FAD}} || {{nowrap|8209 2801 8E5F}} || {{nowrap|8209 2804 8D10}} || {{nowrap|8209 2807 8BB8}} || {{nowrap|8209 280A 8A57}} || {{nowrap|8209 280D 88F6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 3}} || {{nowrap|8209 27FE 92EB}} || {{nowrap|8209 2801 919C}} || {{nowrap|8209 2804 904E}} || {{nowrap|8209 2807 8EFB}} || {{nowrap|8209 280A 8D9E}} || {{nowrap|8209 280D 8C3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 3}} || {{nowrap|8209 27FE 962A}} || {{nowrap|8209 2801 94D8}} || {{nowrap|8209 2804 938B}} || {{nowrap|8209 2807 923B}} || {{nowrap|8209 280A 90E3}} || {{nowrap|8209 280D 8F82}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 1}} || {{nowrap|8209 27FE 996B}} || {{nowrap|8209 2801 9816}} || {{nowrap|8209 2804 96C7}} || {{nowrap|8209 2807 9579}} || {{nowrap|8209 280A 9425}} || {{nowrap|8209 280D 92C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 30}} || {{nowrap|8209 27FE 9CAF}} || {{nowrap|8209 2801 9B55}} || {{nowrap|8209 2804 9A04}} || {{nowrap|8209 2807 98B7}} || {{nowrap|8209 280A 9766}} || {{nowrap|8209 280D 960E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 29}} || {{nowrap|8209 27FE 9FF6}} || {{nowrap|8209 2801 9E98}} || {{nowrap|8209 2804 9D43}} || {{nowrap|8209 2807 9BF5}} || {{nowrap|8209 280A 9AA6}} || {{nowrap|8209 280D 9952}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 28}} || {{nowrap|8209 27FE A33F}} || {{nowrap|8209 2801 A1DE}} || {{nowrap|8209 2804 A084}} || {{nowrap|8209 2807 9F33}} || {{nowrap|8209 280A 9DE5}} || {{nowrap|8209 280D 9C95}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 27}} || {{nowrap|8209 27FE A689}} || {{nowrap|8209 2801 A527}} || {{nowrap|8209 2804 A3C9}} || {{nowrap|8209 2807 A274}} || {{nowrap|8209 280A A125}} || {{nowrap|8209 280D 9FD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 27}} || {{nowrap|8209 27FE A9D2}} || {{nowrap|8209 2801 A872}} || {{nowrap|8209 2804 A711}} || {{nowrap|8209 2807 A5B7}} || {{nowrap|8209 280A A466}} || {{nowrap|8209 280D A318}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1990}} || {{nowrap|2009}} || {{nowrap|2028}} || {{nowrap|2047}} || {{nowrap|2066}} || {{nowrap|2085}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 25}} || {{nowrap|8209 27FE AD19}} || {{nowrap|8209 2801 ABBD}} || {{nowrap|8209 2804 AA5B}} || {{nowrap|8209 2807 A8FD}} || {{nowrap|8209 280A A7A8}} || {{nowrap|8209 280D A65A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 24}} || {{nowrap|8209 27FE B05D}} || {{nowrap|8209 2801 AF06}} || {{nowrap|8209 2804 ADA6}} || {{nowrap|8209 2807 AC45}} || {{nowrap|8209 280A AAEB}} || {{nowrap|8209 280D A99A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 25}} || {{nowrap|8209 27FE B39E}} || {{nowrap|8209 2801 B24B}} || {{nowrap|8209 2804 B0EF}} || {{nowrap|8209 2807 AF8D}} || {{nowrap|8209 280A AE2F}} || {{nowrap|8209 280D ACDA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 24}} || {{nowrap|8209 27FE B6DD}} || {{nowrap|8209 2801 B58D}} || {{nowrap|8209 2804 B436}} || {{nowrap|8209 2807 B2D5}} || {{nowrap|8209 280A B174}} || {{nowrap|8209 280D B01A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 23}} || {{nowrap|8209 27FE BA19}} || {{nowrap|8209 2801 B8CB}} || {{nowrap|8209 2804 B778}} || {{nowrap|8209 2807 B61C}} || {{nowrap|8209 280A B4BA}} || {{nowrap|8209 280D B35C}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 22}} || {{nowrap|8209 27FE BD56}} || {{nowrap|8209 2801 BC08}} || {{nowrap|8209 2804 BAB9}} || {{nowrap|8209 2807 B961}} || {{nowrap|8209 280A B801}} || {{nowrap|8209 280D B69F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 21}} || {{nowrap|8209 27FE C093}} || {{nowrap|8209 2801 BF45}} || {{nowrap|8209 2804 BDF7}} || {{nowrap|8209 2807 BCA4}} || {{nowrap|8209 280A BB47}} || {{nowrap|8209 280D B9E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 20}} || {{nowrap|8209 27FE C3D3}} || {{nowrap|8209 2801 C282}} || {{nowrap|8209 2804 C134}} || {{nowrap|8209 2807 BFE4}} || {{nowrap|8209 280A BE8C}} || {{nowrap|8209 280D BD2B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 18}} || {{nowrap|8209 27FE C716}} || {{nowrap|8209 2801 C5C0}} || {{nowrap|8209 2804 C471}} || {{nowrap|8209 2807 C323}} || {{nowrap|8209 280A C1CF}} || {{nowrap|8209 280D C072}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 18}} || {{nowrap|8209 27FE CA5B}} || {{nowrap|8209 2801 C901}} || {{nowrap|8209 2804 C7B0}} || {{nowrap|8209 2807 C662}} || {{nowrap|8209 280A C511}} || {{nowrap|8209 280D C3B9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 16}} || {{nowrap|8209 27FE CDA4}} || {{nowrap|8209 2801 CC45}} || {{nowrap|8209 2804 CAF0}} || {{nowrap|8209 2807 C9A1}} || {{nowrap|8209 280A C853}} || {{nowrap|8209 280D C6FF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 16}} || {{nowrap|8209 27FE D0EF}} || {{nowrap|8209 2801 CF8D}} || {{nowrap|8209 2804 CE33}} || {{nowrap|8209 2807 CCE2}} || {{nowrap|8209 280A CB94}} || {{nowrap|8209 280D CA44}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1991}} || {{nowrap|2010}} || {{nowrap|2029}} || {{nowrap|2048}} || {{nowrap|2067}} || {{nowrap|2086}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 14}} || {{nowrap|8209 27FE D43A}} || {{nowrap|8209 2801 D2D8}} || {{nowrap|8209 2804 D179}} || {{nowrap|8209 2807 D024}} || {{nowrap|8209 280A CED5}} || {{nowrap|8209 280D CD87}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 13}} || {{nowrap|8209 27FE D783}} || {{nowrap|8209 2801 D623}} || {{nowrap|8209 2804 D4C2}} || {{nowrap|8209 2807 D368}} || {{nowrap|8209 280A D216}} || {{nowrap|8209 280D D0C8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 14}} || {{nowrap|8209 27FE DAC8}} || {{nowrap|8209 2801 D96D}} || {{nowrap|8209 2804 D80B}} || {{nowrap|8209 2807 D6AC}} || {{nowrap|8209 280A D557}} || {{nowrap|8209 280D D408}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 13}} || {{nowrap|8209 27FE DE0A}} || {{nowrap|8209 2801 DCB3}} || {{nowrap|8209 2804 DB53}} || {{nowrap|8209 2807 D9F2}} || {{nowrap|8209 280A D898}} || {{nowrap|8209 280D D747}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 12}} || {{nowrap|8209 27FE E149}} || {{nowrap|8209 2801 DFF6}} || {{nowrap|8209 2804 DE9B}} || {{nowrap|8209 2807 DD38}} || {{nowrap|8209 280A DBDA}} || {{nowrap|8209 280D DA85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 11}} || {{nowrap|8209 27FE E486}} || {{nowrap|8209 2801 E336}} || {{nowrap|8209 2804 E1DF}} || {{nowrap|8209 2807 E07F}} || {{nowrap|8209 280A DF1E}} || {{nowrap|8209 280D DDC4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 10}} || {{nowrap|8209 27FE E7C2}} || {{nowrap|8209 2801 E675}} || {{nowrap|8209 2804 E522}} || {{nowrap|8209 2807 E3C5}} || {{nowrap|8209 280A E263}} || {{nowrap|8209 280D E105}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 9}} || {{nowrap|8209 27FE EAFF}} || {{nowrap|8209 2801 E9B1}} || {{nowrap|8209 2804 E862}} || {{nowrap|8209 2807 E70A}} || {{nowrap|8209 280A E5AA}} || {{nowrap|8209 280D E448}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 8}} || {{nowrap|8209 27FE EE3D}} || {{nowrap|8209 2801 ECEE}} || {{nowrap|8209 2804 EBA0}} || {{nowrap|8209 2807 EA4D}} || {{nowrap|8209 280A E8F0}} || {{nowrap|8209 280D E78E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 7}} || {{nowrap|8209 27FE F17E}} || {{nowrap|8209 2801 F02C}} || {{nowrap|8209 2804 EEDE}} || {{nowrap|8209 2807 ED8E}} || {{nowrap|8209 280A EC36}} || {{nowrap|8209 280D EAD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 6}} || {{nowrap|8209 27FE F4C2}} || {{nowrap|8209 2801 F36C}} || {{nowrap|8209 2804 F21D}} || {{nowrap|8209 2807 F0CF}} || {{nowrap|8209 280A EF7C}} || {{nowrap|8209 280D EE1F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 5}} || {{nowrap|8209 27FE F80A}} || {{nowrap|8209 2801 F6AF}} || {{nowrap|8209 2804 F55E}} || {{nowrap|8209 2807 F410}} || {{nowrap|8209 280A F2C0}} || {{nowrap|8209 280D F168}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1992}} || {{nowrap|2011}} || {{nowrap|2030}} || {{nowrap|2049}} || {{nowrap|2068}} || {{nowrap|2087}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 4}} || {{nowrap|8209 27FE FB55}} || {{nowrap|8209 2801 F9F6}} || {{nowrap|8209 2804 F8A0}} || {{nowrap|8209 2807 F751}} || {{nowrap|8209 280A F603}} || {{nowrap|8209 280D F4B0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 2}} || {{nowrap|8209 27FE FEA0}} || {{nowrap|8209 2801 FD3F}} || {{nowrap|8209 2804 FBE4}} || {{nowrap|8209 2807 FA92}} || {{nowrap|8209 280A F944}} || {{nowrap|8209 280D F7F4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 3}} || {{nowrap|8209 27FF 01EA}} || {{nowrap|8209 2802 0088}} || {{nowrap|8209 2804 FF29}} || {{nowrap|8209 2807 FDD3}} || {{nowrap|8209 280A FC84}} || {{nowrap|8209 280D FB36}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 2}} || {{nowrap|8209 27FF 0531}} || {{nowrap|8209 2802 03D1}} || {{nowrap|8209 2805 0270}} || {{nowrap|8209 2808 0115}} || {{nowrap|8209 280A FFC3}} || {{nowrap|8209 280D FE76}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 1}} || {{nowrap|8209 27FF 0874}} || {{nowrap|8209 2802 0719}} || {{nowrap|8209 2805 05B7}} || {{nowrap|8209 2808 0458}} || {{nowrap|8209 280B 0302}} || {{nowrap|8209 280E 01B4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 27FF 0BB4}} || {{nowrap|8209 2802 0A5E}} || {{nowrap|8209 2805 08FE}} || {{nowrap|8209 2808 079C}} || {{nowrap|8209 280B 0642}} || {{nowrap|8209 280E 04F1}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 27FF 0EF2}} || {{nowrap|8209 2802 0DA0}} || {{nowrap|8209 2805 0C44}} || {{nowrap|8209 2808 0AE2}} || {{nowrap|8209 280B 0984}} || {{nowrap|8209 280E 082F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 29}} || {{nowrap|8209 27FF 122F}} || {{nowrap|8209 2802 10DF}} || {{nowrap|8209 2805 0F88}} || {{nowrap|8209 2808 0E28}} || {{nowrap|8209 280B 0CC7}} || {{nowrap|8209 280E 0B6D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 27}} || {{nowrap|8209 27FF 156B}} || {{nowrap|8209 2802 141D}} || {{nowrap|8209 2805 12CA}} || {{nowrap|8209 2808 116E}} || {{nowrap|8209 280B 100C}} || {{nowrap|8209 280E 0EAE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 26}} || {{nowrap|8209 27FF 18A9}} || {{nowrap|8209 2802 175B}} || {{nowrap|8209 2805 160B}} || {{nowrap|8209 2808 14B4}} || {{nowrap|8209 280B 1353}} || {{nowrap|8209 280E 11F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 25}} || {{nowrap|8209 27FF 1BE9}} || {{nowrap|8209 2802 1A9A}} || {{nowrap|8209 2805 194C}} || {{nowrap|8209 2808 17F9}} || {{nowrap|8209 280B 169C}} || {{nowrap|8209 280E 153A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 24}} || {{nowrap|8209 27FF 1F2C}} || {{nowrap|8209 2802 1DDA}} || {{nowrap|8209 2805 1C8C}} || {{nowrap|8209 2808 1B3D}} || {{nowrap|8209 280B 19E5}} || {{nowrap|8209 280E 1885}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 24}} || {{nowrap|8209 27FF 2272}} || {{nowrap|8209 2802 211C}} || {{nowrap|8209 2805 1FCD}} || {{nowrap|8209 2808 1E7F}} || {{nowrap|8209 280B 1D2C}} || {{nowrap|8209 280E 1BCF}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1993}} || {{nowrap|2012}} || {{nowrap|2031}} || {{nowrap|2050}} || {{nowrap|2069}} || {{nowrap|2088}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 22}} || {{nowrap|8209 27FF 2905}} || {{nowrap|8209 2802 2460}} || {{nowrap|8209 2805 230E}} || {{nowrap|8209 2808 21C0}} || {{nowrap|8209 280B 2070}} || {{nowrap|8209 280E 1F19}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 21}} || {{nowrap|8209 27FF 2C4F}} || {{nowrap|8209 2802 27A6}} || {{nowrap|8209 2805 2650}} || {{nowrap|8209 2808 2500}} || {{nowrap|8209 280B 23B2}} || {{nowrap|8209 280E 225F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 22}} || {{nowrap|8209 27FF 2F97}} || {{nowrap|8209 2802 2AED}} || {{nowrap|8209 2805 2992}} || {{nowrap|8209 2808 2840}} || {{nowrap|8209 280B 26F2}} || {{nowrap|8209 280E 25A2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 21}} || {{nowrap|8209 27FF 32DC}} || {{nowrap|8209 2802 2E35}} || {{nowrap|8209 2805 2CD6}} || {{nowrap|8209 2808 2B80}} || {{nowrap|8209 280B 2A31}} || {{nowrap|8209 280E 28E3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 20}} || {{nowrap|8209 27FF 361E}} || {{nowrap|8209 2802 317D}} || {{nowrap|8209 2805 301B}} || {{nowrap|8209 2808 2EC0}} || {{nowrap|8209 280B 2D6E}} || {{nowrap|8209 280E 2C21}}
|- style=&quot;font-size:small:small;background-color:#ffff00;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 19}} || {{nowrap|8209 27FF 395D}} || {{nowrap|8209 2802 34C3}} || {{nowrap|8209 2805 3361}} || {{nowrap|8209 2808 3202}} || {{nowrap|8209 280B 30AC}} || {{nowrap|8209 280E 2F5E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 18}} || {{nowrap|8209 27FF 3C9B}} || {{nowrap|8209 2802 3807}} || {{nowrap|8209 2805 36A7}} || {{nowrap|8209 2808 3545}} || {{nowrap|8209 280B 33EB}} || {{nowrap|8209 280E 329A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 16}} || {{nowrap|8209 27FF 3FD8}} || {{nowrap|8209 2802 3B48}} || {{nowrap|8209 2805 39ED}} || {{nowrap|8209 2808 388A}} || {{nowrap|8209 280B 372C}} || {{nowrap|8209 280E 35D7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 15}} || {{nowrap|8209 27FF 4316}} || {{nowrap|8209 2802 3E89}} || {{nowrap|8209 2805 3D31}} || {{nowrap|8209 2808 3BD1}} || {{nowrap|8209 280B 3A70}} || {{nowrap|8209 280E 3916}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 14}} || {{nowrap|8209 27FF 4656}} || {{nowrap|8209 2802 41C8}} || {{nowrap|8209 2805 4076}} || {{nowrap|8209 2808 3F1A}} || {{nowrap|8209 280B 3DB8}} || {{nowrap|8209 280E 3C59}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4508}} || {{nowrap|8209 2805 43B9}} || {{nowrap|8209 2808 4262}} || {{nowrap|8209 280B 4102}} || {{nowrap|8209 280E 3FA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 13}} || {{nowrap|8209 27FF 4998}} || {{nowrap|8209 2802 4849}} || {{nowrap|8209 2805 46FB}} || {{nowrap|8209 2808 45A8}} || {{nowrap|8209 280B 444C}} || {{nowrap|8209 280E 42EA}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1994}} || {{nowrap|2013}} || {{nowrap|2032}} || {{nowrap|2051}} || {{nowrap|2070}} || {{nowrap|2089}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 11}} || {{nowrap|8209 27FF 4CDD}} || {{nowrap|8209 2802 4B8A}} || {{nowrap|8209 2805 4A3C}} || {{nowrap|8209 2808 48ED}} || {{nowrap|8209 280B 4795}} || {{nowrap|8209 280E 4635}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 10}} || {{nowrap|8209 27FF 5023}} || {{nowrap|8209 2802 4ECC}} || {{nowrap|8209 2805 4D7D}} || {{nowrap|8209 2808 4C2F}} || {{nowrap|8209 280B 4ADC}} || {{nowrap|8209 280E 4980}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 11}} || {{nowrap|8209 27FF 536B}} || {{nowrap|8209 2802 520F}} || {{nowrap|8209 2805 50BD}} || {{nowrap|8209 2808 4F6F}} || {{nowrap|8209 280B 4E1F}} || {{nowrap|8209 280E 4CC8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 10}} || {{nowrap|8209 27FF 56B3}} || {{nowrap|8209 2802 5553}} || {{nowrap|8209 2805 53FD}} || {{nowrap|8209 2808 52AE}} || {{nowrap|8209 280B 5160}} || {{nowrap|8209 280E 500D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 9}} || {{nowrap|8209 27FF 59FB}} || {{nowrap|8209 2802 5899}} || {{nowrap|8209 2805 573E}} || {{nowrap|8209 2808 55EC}} || {{nowrap|8209 280B 549E}} || {{nowrap|8209 280E 534F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 8}} || {{nowrap|8209 27FF 5D41}} || {{nowrap|8209 2802 5BDF}} || {{nowrap|8209 2805 5A80}} || {{nowrap|8209 2808 592A}} || {{nowrap|8209 280B 57DB}} || {{nowrap|8209 280E 568D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 7}} || {{nowrap|8209 27FF 6085}} || {{nowrap|8209 2802 5F26}} || {{nowrap|8209 2805 5DC4}} || {{nowrap|8209 2808 5C69}} || {{nowrap|8209 280B 5B17}} || {{nowrap|8209 280E 59C9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 6}} || {{nowrap|8209 27FF 63C6}} || {{nowrap|8209 2802 626B}} || {{nowrap|8209 2805 6109}} || {{nowrap|8209 2808 5FAA}} || {{nowrap|8209 280B 5E54}} || {{nowrap|8209 280E 5D06}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 4}} || {{nowrap|8209 27FF 6706}} || {{nowrap|8209 2802 65AF}} || {{nowrap|8209 2805 6450}} || {{nowrap|8209 2808 62EE}} || {{nowrap|8209 280B 6194}} || {{nowrap|8209 280E 6043}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 4}} || {{nowrap|8209 27FF 6A45}} || {{nowrap|8209 2802 68F3}} || {{nowrap|8209 2805 6797}} || {{nowrap|8209 2808 6635}} || {{nowrap|8209 280B 64D7}} || {{nowrap|8209 280E 6382}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 2}} || {{nowrap|8209 27FF 6D85}} || {{nowrap|8209 2802 6C35}} || {{nowrap|8209 2805 6ADF}} || {{nowrap|8209 2808 697F}} || {{nowrap|8209 280B 681D}} || {{nowrap|8209 280E 66C4}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 2}} || {{nowrap|8209 27FF 70C5}} || {{nowrap|8209 2802 6F77}} || {{nowrap|8209 2805 6E25}} || {{nowrap|8209 2808 6CC9}} || {{nowrap|8209 280B 6B67}} || {{nowrap|8209 280E 6A08}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1995}} || {{nowrap|2014}} || {{nowrap|2033}} || {{nowrap|2052}} || {{nowrap|2071}} || {{nowrap|2090}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 1}} || {{nowrap|8209 27FF 7748}} || {{nowrap|8209 2802 72B8}} || {{nowrap|8209 2805 7169}} || {{nowrap|8209 2808 7012}} || {{nowrap|8209 280B 6EB2}} || {{nowrap|8209 280E 6D50}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 30}} || {{nowrap|8209 27FF 7A8C}} || {{nowrap|8209 2802 75F9}} || {{nowrap|8209 2805 74AB}} || {{nowrap|8209 2808 7358}} || {{nowrap|8209 280B 71FD}} || {{nowrap|8209 280E 709B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 1}} || {{nowrap|8209 27FF 7DD1}} || {{nowrap|8209 2802 7939}} || {{nowrap|8209 2805 77EB}} || {{nowrap|8209 2808 769C}} || {{nowrap|8209 280B 7545}} || {{nowrap|8209 280E 73E5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 30}} || {{nowrap|8209 27FF 8117}} || {{nowrap|8209 2802 7C7A}} || {{nowrap|8209 2805 7B2A}} || {{nowrap|8209 2808 79DD}} || {{nowrap|8209 280B 788A}} || {{nowrap|8209 280E 772F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 29}} || {{nowrap|8209 27FF 845E}} || {{nowrap|8209 2802 7FBB}} || {{nowrap|8209 2805 7E69}} || {{nowrap|8209 2808 7D1B}} || {{nowrap|8209 280B 7BCC}} || {{nowrap|8209 280E 7A75}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 28}} || {{nowrap|8209 27FF 87A4}} || {{nowrap|8209 2802 82FE}} || {{nowrap|8209 2805 81A8}} || {{nowrap|8209 2808 8058}} || {{nowrap|8209 280B 7F0A}} || {{nowrap|8209 280E 7DB8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 26}} || {{nowrap|8209 27FF 8AE9}} || {{nowrap|8209 2802 8642}} || {{nowrap|8209 2805 84E7}} || {{nowrap|8209 2808 8395}} || {{nowrap|8209 280B 8247}} || {{nowrap|8209 280E 80F7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 26}} || {{nowrap|8209 27FF 8E2D}} || {{nowrap|8209 2802 8988}} || {{nowrap|8209 2805 8828}} || {{nowrap|8209 2808 86D2}} || {{nowrap|8209 280B 8583}} || {{nowrap|8209 280E 8435}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 24}} || {{nowrap|8209 27FF 9170}} || {{nowrap|8209 2802 8CCE}} || {{nowrap|8209 2805 8B6C}} || {{nowrap|8209 2808 8A11}} || {{nowrap|8209 280B 88C0}} || {{nowrap|8209 280E 8772}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 22}} || {{nowrap|8209 27FF 94B2}} || {{nowrap|8209 2802 9015}} || {{nowrap|8209 2805 8EB3}} || {{nowrap|8209 2808 8D54}} || {{nowrap|8209 280B 8BFF}} || {{nowrap|8209 280E 8AB0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 22}} || {{nowrap|8209 27FF 97F3}} || {{nowrap|8209 2802 935C}} || {{nowrap|8209 2805 91FC}} || {{nowrap|8209 2808 909B}} || {{nowrap|8209 280B 8F40}} || {{nowrap|8209 280E 8DEF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 96A1}} || {{nowrap|8209 2805 9546}} || {{nowrap|8209 2808 93E4}} || {{nowrap|8209 280B 9285}} || {{nowrap|8209 280E 912F}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 21}} || {{nowrap|8209 27FF 9B34}} || {{nowrap|8209 2802 99E5}} || {{nowrap|8209 2805 988E}} || {{nowrap|8209 2808 972F}} || {{nowrap|8209 280B 95CD}} || {{nowrap|8209 280E 9473}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|1996}} || {{nowrap|2015}} || {{nowrap|2034}} || {{nowrap|2053}} || {{nowrap|2072}} || {{nowrap|2091}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 19}} || {{nowrap|8209 27FF 9E74}} || {{nowrap|8209 2802 9D27}} || {{nowrap|8209 2805 9BD4}} || {{nowrap|8209 2808 9A79}} || {{nowrap|8209 280B 9917}} || {{nowrap|8209 280E 97B8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 18}} || {{nowrap|8209 27FF A1B5}} || {{nowrap|8209 2802 A067}} || {{nowrap|8209 2805 9F18}} || {{nowrap|8209 2808 9DC2}} || {{nowrap|8209 280B 9C62}} || {{nowrap|8209 280E 9B01}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 19}} || {{nowrap|8209 27FF A4F7}} || {{nowrap|8209 2802 A3A7}} || {{nowrap|8209 2805 A259}} || {{nowrap|8209 2808 A107}} || {{nowrap|8209 280B 9FAC}} || {{nowrap|8209 280E 9E4A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 17}} || {{nowrap|8209 27FF A839}} || {{nowrap|8209 2802 A6E6}} || {{nowrap|8209 2805 A598}} || {{nowrap|8209 2808 A449}} || {{nowrap|8209 280B A2F3}} || {{nowrap|8209 280E A193}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 17}} || {{nowrap|8209 27FF AB7C}} || {{nowrap|8209 2802 AA25}} || {{nowrap|8209 2805 A8D6}} || {{nowrap|8209 2808 A788}} || {{nowrap|8209 280B A635}} || {{nowrap|8209 280E A4DA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 16}} || {{nowrap|8209 27FF AEC1}} || {{nowrap|8209 2802 AD65}} || {{nowrap|8209 2805 AC12}} || {{nowrap|8209 2808 AAC4}} || {{nowrap|8209 280B A975}} || {{nowrap|8209 280E A81E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 15}} || {{nowrap|8209 27FF B206}} || {{nowrap|8209 2802 B0A6}} || {{nowrap|8209 2805 AF50}} || {{nowrap|8209 2808 AE00}} || {{nowrap|8209 280B ACB3}} || {{nowrap|8209 280E AB60}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 14}} || {{nowrap|8209 27FF B54C}} || {{nowrap|8209 2802 B3EA}} || {{nowrap|8209 2805 B28F}} || {{nowrap|8209 2808 B13D}} || {{nowrap|8209 280B AFEF}} || {{nowrap|8209 280E AEA0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 12}} || {{nowrap|8209 27FF B893}} || {{nowrap|8209 2802 B731}} || {{nowrap|8209 2805 B5D2}} || {{nowrap|8209 2808 B47C}} || {{nowrap|8209 280B B32D}} || {{nowrap|8209 280E B1DF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 11}} || {{nowrap|8209 27FF BBD9}} || {{nowrap|8209 2802 BA7A}} || {{nowrap|8209 2805 B918}} || {{nowrap|8209 2808 B7BD}} || {{nowrap|8209 280B B66B}} || {{nowrap|8209 280E B51E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 10}} || {{nowrap|8209 27FF BF1E}} || {{nowrap|8209 2802 BDC3}} || {{nowrap|8209 2805 BC61}} || {{nowrap|8209 2808 BB02}} || {{nowrap|8209 280B B9AC}} || {{nowrap|8209 280E B85D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 9}} || {{nowrap|8209 27FF C261}} || {{nowrap|8209 2802 C10B}} || {{nowrap|8209 2805 BFAC}} || {{nowrap|8209 2808 BE4A}} || {{nowrap|8209 280B BCEF}} || {{nowrap|8209 280E BB9D}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1997}} || {{nowrap|2016}} || {{nowrap|2035}} || {{nowrap|2054}} || {{nowrap|2073}} || {{nowrap|2092}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 8}} || {{nowrap|8209 27FF C5A2}} || {{nowrap|8209 2802 C451}} || {{nowrap|8209 2805 C2F6}} || {{nowrap|8209 2808 C194}} || {{nowrap|8209 280B C035}} || {{nowrap|8209 280E BEDF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 7}} || {{nowrap|8209 27FF C8E3}} || {{nowrap|8209 2802 C794}} || {{nowrap|8209 2805 C63F}} || {{nowrap|8209 2808 C4E0}} || {{nowrap|8209 280B C37E}} || {{nowrap|8209 280E C223}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 8}} || {{nowrap|8209 27FF CC23}} || {{nowrap|8209 2802 CAD6}} || {{nowrap|8209 2805 C984}} || {{nowrap|8209 2808 C82A}} || {{nowrap|8209 280B C6C8}} || {{nowrap|8209 280E C569}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 6}} || {{nowrap|8209 27FF CF63}} || {{nowrap|8209 2802 CE15}} || {{nowrap|8209 2805 CCC6}} || {{nowrap|8209 2808 CB70}} || {{nowrap|8209 280B CA11}} || {{nowrap|8209 280E C8AF}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 6}} || {{nowrap|8209 27FF D2A3}} || {{nowrap|8209 2802 D153}} || {{nowrap|8209 2805 D005}} || {{nowrap|8209 2808 CEB3}} || {{nowrap|8209 280B CD58}} || {{nowrap|8209 280E CBF6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 5}} || {{nowrap|8209 27FF D5E3}} || {{nowrap|8209 2802 D490}} || {{nowrap|8209 2805 D342}} || {{nowrap|8209 2808 D1F3}} || {{nowrap|8209 280B D09C}} || {{nowrap|8209 280E CF3D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 4}} || {{nowrap|8209 27FF D925}} || {{nowrap|8209 2802 D7CD}} || {{nowrap|8209 2805 D67E}} || {{nowrap|8209 2808 D530}} || {{nowrap|8209 280B D3DE}} || {{nowrap|8209 280E D283}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 2}} || {{nowrap|8209 27FF DC69}} || {{nowrap|8209 2802 DB0D}} || {{nowrap|8209 2805 D9BB}} || {{nowrap|8209 2808 D86D}} || {{nowrap|8209 280B D71E}} || {{nowrap|8209 280E D5C7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 1}} || {{nowrap|8209 27FF DFB0}} || {{nowrap|8209 2802 DE50}} || {{nowrap|8209 2805 DCF9}} || {{nowrap|8209 2808 DBAA}} || {{nowrap|8209 280B DA5C}} || {{nowrap|8209 280E D90A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 1}} || {{nowrap|8209 27FF E2F8}} || {{nowrap|8209 2802 E196}} || {{nowrap|8209 2805 E03A}} || {{nowrap|8209 2808 DEE8}} || {{nowrap|8209 280B DD9A}} || {{nowrap|8209 280E DC4B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 30}} || {{nowrap|8209 27FF E640}} || {{nowrap|8209 2802 E4DE}} || {{nowrap|8209 2805 E37F}} || {{nowrap|8209 2808 E228}} || {{nowrap|8209 280B E0D9}} || {{nowrap|8209 280E DF8B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 29}} || {{nowrap|8209 27FF E987}} || {{nowrap|8209 2802 E829}} || {{nowrap|8209 2805 E6C7}} || {{nowrap|8209 2808 E56B}} || {{nowrap|8209 280B E419}} || {{nowrap|8209 280E E2CB}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 28}} || {{nowrap|8209 27FF ECCD}} || {{nowrap|8209 2802 EB73}} || {{nowrap|8209 2805 EA11}} || {{nowrap|8209 2808 E8B1}} || {{nowrap|8209 280B E75B}} || {{nowrap|8209 280E E60C}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1998}} || {{nowrap|2017}} || {{nowrap|2036}} || {{nowrap|2055}} || {{nowrap|2074}} || {{nowrap|2093}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 27}} || {{nowrap|8209 27FF F010}} || {{nowrap|8209 2802 EEBB}} || {{nowrap|8209 2805 ED5C}} || {{nowrap|8209 2808 EBFB}} || {{nowrap|8209 280B EA9F}} || {{nowrap|8209 280E E94D}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 25}} || {{nowrap|8209 27FF F352}} || {{nowrap|8209 2802 F201}} || {{nowrap|8209 2805 F0A7}} || {{nowrap|8209 2808 EF45}} || {{nowrap|8209 280B EDE5}} || {{nowrap|8209 280E EC8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 27}} || {{nowrap|8209 27FF F692}} || {{nowrap|8209 2802 F543}} || {{nowrap|8209 2805 F3EE}} || {{nowrap|8209 2808 F28F}} || {{nowrap|8209 280B F12D}} || {{nowrap|8209 280E EFD2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 25}} || {{nowrap|8209 27FF F9D0}} || {{nowrap|8209 2802 F882}} || {{nowrap|8209 2805 F731}} || {{nowrap|8209 2808 F5D6}} || {{nowrap|8209 280B F474}} || {{nowrap|8209 280E F315}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 25}} || {{nowrap|8209 27FF FD0D}} || {{nowrap|8209 2802 FBBF}} || {{nowrap|8209 2805 FA70}} || {{nowrap|8209 2808 F91A}} || {{nowrap|8209 280B F7BB}} || {{nowrap|8209 280E F659}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 23}} || {{nowrap|8209 2800 004B}} || {{nowrap|8209 2802 FEFB}} || {{nowrap|8209 2805 FDAE}} || {{nowrap|8209 2808 FC5C}} || {{nowrap|8209 280B FB01}} || {{nowrap|8209 280E F99F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 23}} || {{nowrap|8209 2800 038B}} || {{nowrap|8209 2803 0238}} || {{nowrap|8209 2806 00EA}} || {{nowrap|8209 2808 FF9B}} || {{nowrap|8209 280B FE45}} || {{nowrap|8209 280E FCE6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 21}} || {{nowrap|8209 2800 06CE}} || {{nowrap|8209 2803 0576}} || {{nowrap|8209 2806 0427}} || {{nowrap|8209 2809 02D9}} || {{nowrap|8209 280C 0187}} || {{nowrap|8209 280F 002C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 20}} || {{nowrap|8209 2800 0A14}} || {{nowrap|8209 2803 08B8}} || {{nowrap|8209 2806 0765}} || {{nowrap|8209 2809 0617}} || {{nowrap|8209 280C 04C8}} || {{nowrap|8209 280F 0371}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 19}} || {{nowrap|8209 2800 0D5C}} || {{nowrap|8209 2803 0BFC}} || {{nowrap|8209 2806 0AA5}} || {{nowrap|8209 2809 0955}} || {{nowrap|8209 280C 0807}} || {{nowrap|8209 280F 06B5}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 18}} || {{nowrap|8209 2800 10A6}} || {{nowrap|8209 2803 0F44}} || {{nowrap|8209 2806 0DE8}} || {{nowrap|8209 2809 0C95}} || {{nowrap|8209 280C 0B47}} || {{nowrap|8209 280F 09F8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 17}} || {{nowrap|8209 2800 13EF}} || {{nowrap|8209 2803 128E}} || {{nowrap|8209 2806 112E}} || {{nowrap|8209 2809 0FD7}} || {{nowrap|8209 280C 0E87}} || {{nowrap|8209 280F 0D3A}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|1999}} || {{nowrap|2018}} || {{nowrap|2037}} || {{nowrap|2056}} || {{nowrap|2075}} || {{nowrap|2094}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 16}} || {{nowrap|8209 2800 1738}} || {{nowrap|8209 2803 15D9}} || {{nowrap|8209 2806 1477}} || {{nowrap|8209 2809 131B}} || {{nowrap|8209 280C 11C9}} || {{nowrap|8209 280F 107B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 15}} || {{nowrap|8209 2800 1A7D}} || {{nowrap|8209 2803 1924}} || {{nowrap|8209 2806 17C2}} || {{nowrap|8209 2809 1662}} || {{nowrap|8209 280C 150B}} || {{nowrap|8209 280F 13BC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 16}} || {{nowrap|8209 2800 1DC0}} || {{nowrap|8209 2803 1C6B}} || {{nowrap|8209 2806 1B0C}} || {{nowrap|8209 2809 19AA}} || {{nowrap|8209 280C 184F}} || {{nowrap|8209 280F 16FC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 14}} || {{nowrap|8209 2800 20FF}} || {{nowrap|8209 2803 1FAE}} || {{nowrap|8209 2806 1E54}} || {{nowrap|8209 2809 1CF3}} || {{nowrap|8209 280C 1B93}} || {{nowrap|8209 280F 1A3C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 14}} || {{nowrap|8209 2800 243C}} || {{nowrap|8209 2803 22EE}} || {{nowrap|8209 2806 2198}} || {{nowrap|8209 2809 203A}} || {{nowrap|8209 280C 1ED8}} || {{nowrap|8209 280F 1D7C}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 13}} || {{nowrap|8209 2800 2779}} || {{nowrap|8209 2803 262B}} || {{nowrap|8209 2806 24DA}} || {{nowrap|8209 2809 2380}} || {{nowrap|8209 280C 221E}} || {{nowrap|8209 280F 20BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 12}} || {{nowrap|8209 2800 2AB6}} || {{nowrap|8209 2803 2968}} || {{nowrap|8209 2806 2819}} || {{nowrap|8209 2809 26C3}} || {{nowrap|8209 280C 2564}} || {{nowrap|8209 280F 2403}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 11}} || {{nowrap|8209 2800 2DF4}} || {{nowrap|8209 2803 2CA4}} || {{nowrap|8209 2806 2B57}} || {{nowrap|8209 2809 2A05}} || {{nowrap|8209 280C 28AA}} || {{nowrap|8209 280F 2748}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 9}} || {{nowrap|8209 2800 3135}} || {{nowrap|8209 2803 2FE2}} || {{nowrap|8209 2806 2E94}} || {{nowrap|8209 2809 2D45}} || {{nowrap|8209 280C 2BEF}} || {{nowrap|8209 280F 2A8F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 9}} || {{nowrap|8209 2800 3479}} || {{nowrap|8209 2803 3322}} || {{nowrap|8209 2806 31D2}} || {{nowrap|8209 2809 3084}} || {{nowrap|8209 280C 2F32}} || {{nowrap|8209 280F 2DD7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 7}} || {{nowrap|8209 2800 37C1}} || {{nowrap|8209 2803 3664}} || {{nowrap|8209 2806 3511}} || {{nowrap|8209 2809 33C3}} || {{nowrap|8209 280C 3274}} || {{nowrap|8209 280F 311E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 6}} || {{nowrap|8209 2800 3B0B}} || {{nowrap|8209 2803 39AA}} || {{nowrap|8209 2806 3853}} || {{nowrap|8209 2809 3703}} || {{nowrap|8209 280C 35B6}} || {{nowrap|8209 280F 3464}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2000}} || {{nowrap|2019}} || {{nowrap|2038}} || {{nowrap|2057}} || {{nowrap|2076}} || {{nowrap|2095}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 5}} || {{nowrap|8209 2800 3E56}} || {{nowrap|8209 2803 3CF4}} || {{nowrap|8209 2806 3B98}} || {{nowrap|8209 2809 3A45}} || {{nowrap|8209 280C 38F7}} || {{nowrap|8209 280F 37A8}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 3}} || {{nowrap|8209 2800 41A0}} || {{nowrap|8209 2803 403F}} || {{nowrap|8209 2806 3EDF}} || {{nowrap|8209 2809 3D88}} || {{nowrap|8209 280C 3C38}} || {{nowrap|8209 280F 3AEA}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 5}} || {{nowrap|8209 2800 44E8}} || {{nowrap|8209 2803 438A}} || {{nowrap|8209 2806 4228}} || {{nowrap|8209 2809 40CB}} || {{nowrap|8209 280C 3F78}} || {{nowrap|8209 280F 3E2A}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 3}} || {{nowrap|8209 2800 482B}} || {{nowrap|8209 2803 46D2}} || {{nowrap|8209 2806 4570}} || {{nowrap|8209 2809 4410}} || {{nowrap|8209 280C 42B9}} || {{nowrap|8209 280F 4169}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 3}} || {{nowrap|8209 2800 4B6B}} || {{nowrap|8209 2803 4A16}} || {{nowrap|8209 2806 48B8}} || {{nowrap|8209 2809 4756}} || {{nowrap|8209 280C 45FA}} || {{nowrap|8209 280F 44A7}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 1}} || {{nowrap|8209 2800 4EA9}} || {{nowrap|8209 2803 4D58}} || {{nowrap|8209 2806 4BFE}} || {{nowrap|8209 2809 4A9D}} || {{nowrap|8209 280C 493D}} || {{nowrap|8209 280F 47E6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 51E5}} || {{nowrap|8209 2803 5097}} || {{nowrap|8209 2806 4F42}} || {{nowrap|8209 2809 4DE3}} || {{nowrap|8209 280C 4C81}} || {{nowrap|8209 280F 4B26}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 1}} || {{nowrap|8209 2800 5522}} || {{nowrap|8209 2803 53D4}} || {{nowrap|8209 2806 5283}} || {{nowrap|8209 2809 5129}} || {{nowrap|8209 280C 4FC7}} || {{nowrap|8209 280F 4E67}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 29}} || {{nowrap|8209 2800 585F}} || {{nowrap|8209 2803 5711}} || {{nowrap|8209 2806 55C2}} || {{nowrap|8209 2809 546D}} || {{nowrap|8209 280C 530E}} || {{nowrap|8209 280F 51AC}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 27}} || {{nowrap|8209 2800 5B9F}} || {{nowrap|8209 2803 5A4F}} || {{nowrap|8209 2806 5901}} || {{nowrap|8209 2809 57AF}} || {{nowrap|8209 280C 5654}} || {{nowrap|8209 280F 54F2}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 27}} || {{nowrap|8209 2800 5EE1}} || {{nowrap|8209 2803 5D8E}} || {{nowrap|8209 2806 5C40}} || {{nowrap|8209 2809 5AF1}} || {{nowrap|8209 280C 599B}} || {{nowrap|8209 280F 583B}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 25}} || {{nowrap|8209 2800 6227}} || {{nowrap|8209 2803 60CF}} || {{nowrap|8209 2806 5F7F}} || {{nowrap|8209 2809 5E32}} || {{nowrap|8209 280C 5CE0}} || {{nowrap|8209 280F 5B85}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 25}} || {{nowrap|8209 2800 6571}} || {{nowrap|8209 2803 6414}} || {{nowrap|8209 2806 62C1}} || {{nowrap|8209 2809 6173}} || {{nowrap|8209 280C 6024}} || {{nowrap|8209 280F 5ECE}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
|| || {{nowrap|2001}} || {{nowrap|2020}} || {{nowrap|2039}} || {{nowrap|2058}} || {{nowrap|2077}} || {{nowrap|2096}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 24}} || {{nowrap|8209 2800 68BC}} || {{nowrap|8209 2803 675C}} || {{nowrap|8209 2806 6604}} || {{nowrap|8209 2809 64B4}} || {{nowrap|8209 280C 6366}} || {{nowrap|8209 280F 6214}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 22}} || {{nowrap|8209 2800 6C07}} || {{nowrap|8209 2803 6AA5}} || {{nowrap|8209 2806 6948}} || {{nowrap|8209 2809 67F5}} || {{nowrap|8209 280C 66A6}} || {{nowrap|8209 280F 6557}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 24}} || {{nowrap|8209 2800 6F4F}} || {{nowrap|8209 2803 6DEE}} || {{nowrap|8209 2806 6C8E}} || {{nowrap|8209 2809 6B36}} || {{nowrap|8209 280C 69E6}} || {{nowrap|8209 280F 6898}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 22}} || {{nowrap|8209 2800 7294}} || {{nowrap|8209 2803 7136}} || {{nowrap|8209 2806 6FD4}} || {{nowrap|8209 2809 6E77}} || {{nowrap|8209 280C 6D24}} || {{nowrap|8209 280F 6BD6}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 22}} || {{nowrap|8209 2800 75D5}} || {{nowrap|8209 2803 747C}} || {{nowrap|8209 2806 731B}} || {{nowrap|8209 2809 71BB}} || {{nowrap|8209 280C 7063}} || {{nowrap|8209 280F 6F14}}
|- style=&quot;font-size:small:small;background-color:#ffaaaa;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 20}} || {{nowrap|8209 2800 7915}} || {{nowrap|8209 2803 77C0}} || {{nowrap|8209 2806 7662}} || {{nowrap|8209 2809 7500}} || {{nowrap|8209 280C 73A4}} || {{nowrap|8209 280F 7251}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 19}} || {{nowrap|8209 2800 7C52}} || {{nowrap|8209 2803 7B01}} || {{nowrap|8209 2806 79A7}} || {{nowrap|8209 2809 7846}} || {{nowrap|8209 280C 76E6}} || {{nowrap|8209 280F 758F}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 18}} || {{nowrap|8209 2800 7F8E}} || {{nowrap|8209 2803 7E40}} || {{nowrap|8209 2806 7CEB}} || {{nowrap|8209 2809 7B8C}} || {{nowrap|8209 280C 7A2A}} || {{nowrap|8209 280F 78CE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 16}} || {{nowrap|8209 2800 82CB}} || {{nowrap|8209 2803 817E}} || {{nowrap|8209 2806 802C}} || {{nowrap|8209 2809 7ED2}} || {{nowrap|8209 280C 7D70}} || {{nowrap|8209 280F 7C11}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 16}} || {{nowrap|8209 2800 860A}} || {{nowrap|8209 2803 84BC}} || {{nowrap|8209 2806 836D}} || {{nowrap|8209 2809 8218}} || {{nowrap|8209 280C 80B9}} || {{nowrap|8209 280F 7F57}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 15}} || {{nowrap|8209 2800 894C}} || {{nowrap|8209 2803 87FB}} || {{nowrap|8209 2806 86AE}} || {{nowrap|8209 2809 855C}} || {{nowrap|8209 280C 8402}} || {{nowrap|8209 280F 82A0}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 14}} || {{nowrap|8209 2800 8C90}} || {{nowrap|8209 2803 8B3D}} || {{nowrap|8209 2806 89EF}} || {{nowrap|8209 2809 88A0}} || {{nowrap|8209 280C 874A}} || {{nowrap|8209 280F 85EC}}
|- style=&quot;background-color: #eaecf0; font-size: large; font-weight: bold;&quot;
||  || {{nowrap|2002}} || {{nowrap|2021}} || {{nowrap|2040}} || {{nowrap|2059}} || {{nowrap|2078}} || {{nowrap|2097}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jan 13}} || {{nowrap|8209 2800 8FD8}} || {{nowrap|8209 2803 8E80}} || {{nowrap|8209 2806 8D30}} || {{nowrap|8209 2809 8BE2}} || {{nowrap|8209 280C 8A90}} || {{nowrap|8209 280F 8936}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Feb 11}} || {{nowrap|8209 2800 9322}} || {{nowrap|8209 2803 91C5}} || {{nowrap|8209 2806 9071}} || {{nowrap|8209 2809 8F23}} || {{nowrap|8209 280C 8DD4}} || {{nowrap|8209 280F 8C7E}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Mar 13}} || {{nowrap|8209 2800 966C}} || {{nowrap|8209 2803 950B}} || {{nowrap|8209 2806 93B2}} || {{nowrap|8209 2809 9262}} || {{nowrap|8209 280C 9114}} || {{nowrap|8209 280F 8FC3}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Apr 11}} || {{nowrap|8209 2800 99B4}} || {{nowrap|8209 2803 9852}} || {{nowrap|8209 2806 96F5}} || {{nowrap|8209 2809 95A1}} || {{nowrap|8209 280C 9453}} || {{nowrap|8209 280F 9305}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|May 11}} || {{nowrap|8209 2800 9CFB}} || {{nowrap|8209 2803 9B9A}} || {{nowrap|8209 2806 9A39}} || {{nowrap|8209 2809 98E1}} || {{nowrap|8209 280C 9791}} || {{nowrap|8209 280F 9644}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jun 9}} || {{nowrap|8209 2800 A03E}} || {{nowrap|8209 2803 9EE1}} || {{nowrap|8209 2806 9D7E}} || {{nowrap|8209 2809 9C22}} || {{nowrap|8209 280C 9ACF}} || {{nowrap|8209 280F 9981}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Jul 9}} || {{nowrap|8209 2800 A37F}} || {{nowrap|8209 2803 A226}} || {{nowrap|8209 2806 A0C4}} || {{nowrap|8209 2809 9F64}} || {{nowrap|8209 280C 9E0C}} || {{nowrap|8209 280F 9CBD}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Aug 7}} || {{nowrap|8209 2800 A6BD}} || {{nowrap|8209 2803 A569}} || {{nowrap|8209 2806 A40A}} || {{nowrap|8209 2809 A2A8}} || {{nowrap|8209 280C A14C}} || {{nowrap|8209 280F 9FF9}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Sep 6}} || {{nowrap|8209 2800 A9FB}} || {{nowrap|8209 2803 A8AA}} || {{nowrap|8209 2806 A750}} || {{nowrap|8209 2809 A5EF}} || {{nowrap|8209 280C A48F}} || {{nowrap|8209 280F A337}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Oct 5}} || {{nowrap|8209 2800 AD39}} || {{nowrap|8209 2803 ABEA}} || {{nowrap|8209 2806 AA95}} || {{nowrap|8209 2809 A937}} || {{nowrap|8209 280C A7D5}} || {{nowrap|8209 280F A679}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Nov 4}} || {{nowrap|8209 2800 B078}} || {{nowrap|8209 2803 AF2A}} || {{nowrap|8209 2806 ADD9}} || {{nowrap|8209 2809 AC7F}} || {{nowrap|8209 280C AB1E}} || {{nowrap|8209 280F A9BE}}
|- style=&quot;font-size:small:small;background-color:#ffffff;”
| style=&quot;font-weight: bold; background-color: #eaecf0;&quot; | {{nowrap|Dec 3}} || {{nowrap|8209 2800 B3B9}} || {{nowrap|8209 2803 B26B}} || {{nowrap|8209 2806 B11C}} || {{nowrap|8209 2809 AFC7}} || {{nowrap|8209 280C AE69}} || {{nowrap|8209 280F AD07}}

|}</text>
      <sha1>h9rnxaiz37ih16c479mqgn5xp47bydd</sha1>
    </revision>
  </page>
  <page>
    <title>Wikiversity:Patrolling</title>
    <ns>4</ns>
    <id>329840</id>
    <revision>
      <id>2815662</id>
      <parentid>2812121</parentid>
      <timestamp>2026-06-14T17:21:37Z</timestamp>
      <contributor>
        <username>Codename Noreste</username>
        <id>2969951</id>
      </contributor>
      <comment>/* Who can patrol? */ +</comment>
      <origin>2815662</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4106" sha1="ne6u04qcgwt7bfv830h477v67es55gt" xml:space="preserve">{{Proposal}}
'''Patrolling''' is trusted user review of newly created pages and recent edits to identify pages that need improvement, administrative attention, deletion, and new contributors who need support.

Patrolling is a collobaritve part of [[Wikiversity:Maintenance|Wikiversity’s maintenance work]]. It is not approval of content, but rather an initial review to identify obvious issues that warrant attention.

Unpatrolled edits show up in [[Special:RecentChanges]] with an exclamation mark (!), while unpatrolled new pages are highlighted in yellow. The ability to patrol is determined by [[Wikiversity:User access levels|user rights]]. Wikiversity also uses an autopatrol right, meaning trusted users' contributions are automatically marked as checked so patrollers can focus on reviewing newer or anonymous editors.

== Purpose ==
Patrolling helps to:
* welcome and support new contributors
* identify pages that may need formatting, categorisation, or wikification
* check whether new pages fit Wikiversity’s educational scope
* identify vandalism, spam, copyright violations, or other problematic content
* reduce the backlog of unreviewed pages
* improve the discoverability and organisation of learning resources

== Who can patrol? ==
Patrolling may be undertaken by users with the appropriate user rights, including:
* [[Wikiversity:Curatorship|Curators]]
* [[Wikiversity:Custodianship|Custodians]]
These users can mark pages as patrolled.

Wikiversity also has an [[Wikiversity:Autopatrollers|autopatroller]] user group, in which trusted users' contributions are automatically marked as patrolled, so that patrollers can focus on reviewing pages from newer or anonymous editors.

== What patrolling means ==
Marking a page as patrolled indicates that the page has received an initial review. This generally means that the patroller has checked that:
* the page is not obvious vandalism or spam
* the page broadly fits Wikiversity’s scope and mission
* the title is reasonable
* the content is not an obvious copyright violation
* any urgent issues have been addressed or flagged for follow-up

Patrolling '''does not''' necessarily mean that the:
* page is complete
* page meets all style guidelines
* content has been fact-checked
* page has community endorsement

Pages can still be edited, improved, moved, nominated for deletion, or discussed after being marked as patrolled.

== Suggested patrolling workflow ==
When reviewing a newly created page, patrollers are encouraged to:
# Open the page and read the content
# Check the page history and creator's contributions
# Consider whether the page is within [[Wikiversity:Scope|Wikiversity’s scope]]
# Look for:
#* vandalism
#* spam or promotional content
#* copyright concerns
#* test pages
#* pages requiring [[Wikiversity:Deletion|speedy deletion]] or cleanup
# If appropriate:
#* add categories
#* add maintenance templates
#* welcome or assist the creator on their talk page
#* nominate the page for deletion if needed
# Mark the page as patrolled once reviewed

== When not to mark a page as patrolled ==
A page should generally '''not''' be marked as patrolled if it:
* is obvious vandalism awaiting reversion or deletion
* is spam or promotional content needing removal
* appears to be a copyright violation
* requires immediate administrative attention and has not yet been addressed

In these cases, patrollers should address or flag the issue first.

== Good practice ==
Patrollers are encouraged to:
* [[Wikiversity:Assume good faith|assume good faith]], especially with new contributors
* focus on whether a page needs attention, rather than whether it is “perfect”
* leave constructive feedback where useful
* use maintenance templates to indicate issues
* discuss borderline cases with the community when unsure

== See also ==
* [[Special:NewPages|New pages]] | [[Special:RecentChanges|Recent changes]]
* [[Wikiversity:Curatorship|Curators]] | [[Wikiversity:Custodianship|Custodians]]
* [[Wikiversity:Scope|Scope]]
* [[Wikiversity:Deletion requests|Deletion requests]]

[[Category:Wikiversity maintenance]]</text>
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    </revision>
  </page>
  <page>
    <title>Talk:Bully Metric</title>
    <ns>1</ns>
    <id>330199</id>
    <revision>
      <id>2815746</id>
      <timestamp>2026-06-15T02:26:46Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Wikipedia links</comment>
      <origin>2815746</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="418" sha1="46ndaj8na1f4dp87slcotda4ly3qaae" xml:space="preserve">==Wikipedia links==
{{ping|Unitfreak}} FYI, I updated the Wikipedia links from external link style to interwiki link style on this page: 
https://en.wikiversity.org/w/index.php?title=Bully_Metric&amp;curid=308469&amp;diff=2815743&amp;oldid=2791845. Consider applying elsewhere. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:26, 15 June 2026 (UTC)</text>
      <sha1>46ndaj8na1f4dp87slcotda4ly3qaae</sha1>
    </revision>
  </page>
</mediawiki>